Question: What I'm trying to say is should Light tell Teru that killing from scrape paper is possible, then if Teru kept a real deathnote paper with him 24/7, surely that in the final showdown, whoever names written on that piece of paper they surely will die, won't they? 

That way you don't even need to worry about the book switching scheme.

Answer: 
Whole point of Teru was to be a decoy. If SPK had seen Mikami using a seperate paper of the real death note would be a give away. For example. Instead of visiting the bank to retrieve the real Deathnote, Megami might have used the paper. Which would still give him away.

Light made sure the Mikami had NO access to the real DeathNote and explicitly said him to only take it out on the D-Day.

This is basically an speculative question containing the What-if Scenarios. You can plausibly say that something might've worked out, but as I have just said above... Chances are it would have blown up more easily. Because SPK would have been dead if Mikami had trusted Light and not gone to retrieve the Real DeathNote from the bank.

EDIT: I get the question was why didn't Mikami keep a seperate real piece of DN paper for the day of the final D-Day instead of the DN. I answered this What-if scenario with a plausible explaination that Mikami may have used it to kill Takada. Then I went on to explain this was why Light didn't want ANY piece of real Death Note with Mikami, to keep the plan full proof. 

**Tl;dr Mikami didn't keep the DN paper because Light told him not to. This was because Light just like Near wanted to play complete and full proof game but lost to the external factors of Mello and Mikami**
This is the email x-kira should be recieved prior to Jan 28th...

In exactly 1 month and 29 days from today, the 26th of January. Do not go to the bank to pick up the note. Instead and I suggest sometime in December. Make 2 copies not one of the notebook. Keep one in your brief case and the other in the bank vault. Keep the original but burry it by using a name to do so for you. That way you cannot be tracked. Then keep a page on you and on the day of 28th January at 1pm. Use this page to rest on the fake that the spk will use. Write down Nate River first. Then kill the rest except light Yagami.

-LY ;]