I have misplaced my trainer bike skewer. Can I use the one from my bike? I am not concerned about scratches.
I wouldn't. You'll damage the skewer you have, which will make it unreliable on the road, if not unusable.
Basic skewers with plastic on the nut will certainly be damaged, the plastic gets crushed and then you can't use it. Even skewers with more expensive metal parts will be subject to forces they weren't designed for. If a nice skewer should be damaged in this way, that is more expensive than the right trainer specific part, it is a false economy.
I should have your LBS order in something suitable
Depends on the trainer.
If the trainer had a special skewers that had ends shaped specifically to fit in the trainer, you can't use a standard skewer. The trainer will not hold the bike properly. The bike coming out of the trainer with you on it would be bad.
If the trainer accepts normal skewers, but supplied a spare so your regular one does not get mashed up, then it's fine. I'd buy a cheap spare and mess that up though.