Bar Keepers friend...mild oxalic acid, won't etch or do any damage if you use it right. Only way it can do any harm is if you leave it sit on.
This stuff will take the tarnish right up without much fuss, it can be wiped off after with a damp towel, let it air dry and yer good to go. It works on silver/nickel silver etc.
The thing is those silvers are probably a very thin plating, so less abrasive is always better. I wouldn't use heavy polishing compounds, pastes or a dremel, only elbow grease.
Try a can of bar keepers...a diluted batch with a saturated q tip should work very well. Then I'd say add a tiny drop of linseed oil and buff by hand it will slow the tarnish down considerably.