Is there any way to stop the trainer from spawning peds with only MP5's?

You'd probably be better off asking in this section: http://www.lcpdfr.com/forum/799-support-requests/

But as far as I can remember there's a weapon option above where you spawn them in the spawn ped menu. If you already set it, I've noticed it doesn't work correctly if you spawn them in too quickly. I recently spawned in a hoard of armed strippers and only half of them had the right weapon since I spammed the 5 key while spawning all of them in. I tried spawning them in one by one with about a second of pause between each one and they all got the right weapon.

Sounds like the peds are spawning with drive by weapons enabled. When selecting the bodyguard/ped scroll down the list until you reach "enable/disable driveby weapon" (or something like that) and change it to "disabled". that should fix it.

^Was about to say that, it really annoyed me too, I just recently found out about it.