First of all, the good news. The silver content of most US Morgan and Peace dollars is usually such that it exceeds the value of the coin as a collectors item. There are however exceptions so check the dates and mint marks carefully and seperate any rare coins.
There are a few companies which can clean coins for you for a hefty fee, not worth except in the case of higher value coins. If any of the dates have a high value this is probably your best option.
The bullion coins, well I would just leave them. If you intend to keep them as part of a collection then you are probably going to ignore the previous advice

Fair enough. If you really, really, intend to clean them it may be simple fabric glue. You could probably peel that off without causing much damage. If it's something stronger then you may have a problem.
Coin supply dealers carry silver cleaners which they claim work but I'm a little skeptical. It's certainly more affordable that having them cleaned professionaly though. Don't try silver polish, the kind you clean teapots with! It will scour the surface badly.
If it's a non solvent glue you may be able to remove it with nothing more than warm water and a soft cloth. Don't rub the coins to dry them, pat them dry to minimise changes to the surface.
You are right, cleaning a coin does detract from it's value as a collectors piece but then so does a big glob of ugly glue. It's a hard call but keep in mind the bullion value won't suffer. Whatever you decide, for heavens sake try it out on a single coin first rather than dipping the whole bunch in "Goo-Off".
Non illegitimis carborundum est. Excellent advice for all coins.
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