Is it permissible for him to wish that Allah will not marry him to al-hoor al-‘iyn in Paradise and to pray for that?
Question

I know that in Paradise the Muslim will be given al-hoor al-‘iyn in sha Allah, but I do not want any hooriyaat in Paradise! I want to be on my own, me and my wife. I am not married yet but I want this wish from Allah, may He be glorified and exalted, that my wife and I will stay on our own in Paradise.
You may think my question is silly but my request is sincere. To be honest I pray to Allah to be in Paradise and I hope that Allah will accept it from me. Is this possible?.
Praise be to Allah.Firstly: 
What you seem to be saying is a transgression in du‘aa’ which means that it is not allowed and the reasons why it is not allowed are many and include the following: 
1.
It is a rejection of the bounty that Allah bestows upon His slaves and the honour that He will bestow upon them in Paradise, and He has told us of the state of bliss in which they will be. In fact your prayer is a rejection of this blessing that Allah will bestow upon those whom He honours with Paradise and encourages them to aspire to it, as He says (interpretation of the meaning):
“Verily! The Muttaqûn (pious), will be in place of Security (Paradise) (51) Among Gardens and Springs; (52) Dressed in fine silk and (also) in thick silk, facing each other, (53) So (it will be), and We shall marry them to Hur (fair females) with wide, lovely eyes.”
[al-Dukhaan 44:51-54]
“Eat and drink with happiness because of what you used to do." (19) They will recline (with ease) on thrones arranged in ranks. And We shall marry them to Hûr (female, fair ones) with wide lovely eyes”
[al-Toor 52:19, 20]
“But those who believe (in the Oneness of Allâh - Islâmic Monotheism) and do deeds of righteousness, We shall admit them to Gardens under which rivers flow (Paradise), abiding therein forever. Therein they shall have Azwâjun Mutahharatun[] [purified mates or wives] and We shall admit them to shades wide and ever deepening (Paradise)”
[al-Nisa’ 4:57]
“And (there will be) Hur (fair females) with wide, lovely eyes (as wives for the pious), (22) Like unto preserved pearls. (23) A reward for what they used to do”
[al-Waaqi ‘ah :22-24]. 
2.
Your supplication not to be married to al-hoor al-‘iyn indicates that you are not aware of the true nature of the blessings that Allah will bestow upon the one for whom He decrees Paradise. The attributes of al-hoor al-‘iyn that Allah has told us of makes the Muslim long to attain this blessing and bounty. The one who limits this bliss only to sex is making a mistake in his understanding of that blessing or is not appreciating it properly. For example it is narrated that al-hoor al-‘iyn will sing for their husbands in Paradise. It was narrated from Ibn ‘Umar (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “The wives of the people of Paradise will sing for their husbands in the most beautiful voices that anyone has ever heard, and one of the things they will say is: We are the good ones, the beautiful ones, the wives of the noble people.”
Narrated by al-Tabaraani in al-Mu‘jam al-Awsat, 5/149; classed as saheeh by al-Albaani in Saheeh al-Targheeb, 3/269.
Another example is her being a good wife to her husband and she will speak softly and gently to him, which will fill his heart with joy; this is what is meant by “Loving (their husbands only)”, [as in al-Waaqi‘ah 56:37].  
Shaykh ‘Abd al-Rahmaan al-Sa‘di (may Allah have mercy on him) said: 
“Loving (their husbands only), (and) of equal age” [al-Waaqi‘ah 56:37] means they will always be like that, in all circumstances. ‘Uroob (translated here as loving) refers to the wife who is loving towards her husband and speaks nicely to him, and looks nice, and is beautiful and kind. She is the one who if she speaks, her speech causes infatuation and the one who hears her wishes that her words will never end, especially when she sings in that sweet voice; and if he looks at her manners, appearance and gentleness, she will fill her husband’s heart with joy and happiness; and if she moves from one place to another, that place is filled with a beautiful fragrance and light. That also includes flirting during intimacy. 
“of equal age” means those who are of the same age, thirty-three years old, which is the peak of growth and the end of the years of youth. So their wives will be “Loving (their husbands only), (and) of equal age”, living together in harmony, pleased and pleasing; they will not grieve or cause grief; rather they will be joyful and delightful.  
End quote from Tafseer al-Sa‘di, p. 833 
3.
It seems that one of the reasons for your wanting to pray for this is that you have been affected by love stories and tales of romance which focus on the love of one party for the other. There is nothing wrong with spouses loving one another; rather this is something desirable and praiseworthy. But exaggerating about that to the point that it puts one off the idea of any other marriage in this world, even though Allah has prescribed it and has connected many worldly interests to it, is something that is objectionable. Moreover, we think that exaggerating about that has gone so far as to include the Hereafter, as he does not want his wife to have any co-wives in Paradise. 
Finally you should note that Paradise is quite different from this world; there is nothing of this world in it apart from names of things. So strive to follow the path that will lead to it and pray to Allah to make you one of its people, then stop comparing it to things in this world and do not restrict the vastness of Allah’s mercy. There – if you are one of its people, in sha Allah – you will realise that things are different. 
And Allah knows best.