Question: I have a new APU and was wondering if putting a small amount of paste on the APU would be too much. if there is too much, will this damage the APU,or will it be fine?

Answer: 
Use a thin layer - remember, all you need to do is to fill in the microscopically small air-spaces between the two surfaces.

Also, don't forget to clean off all the old thermal compound - you can use alcohol or there are cleaners made for the purpose.

Too much thermal paste will lead to increased temperatures, but unless you add a really huge amount, it wouldn't be enough to cause damage via heat. (Besides, modern processors should be able to shut themselves down quickly (theoretically, fast enough to prevent damage) if they detect sufficiently high temperatures.)
The idea of Thermal Paste is to help distribute the heat from one side to the other side. 2 Metal Contact (APU or CPU to heatsink) are not really distributing heat that nicely. The Thermal Paste helps to create a transferring link between the 2 metal contact. 

If you do have a heatsink for the APU, then before applying additional thermal paste, check if the heatsink already have thermal paste. If yes, no need to add more. If none, then add very small amount and spread it out to ensure it is thin and even across the metal contact to the heatsink.

If the APU does not use any heatsink, then why are you applying thermal paste?