Somewhere on the battery charger will be a label giving the working voltage of your battery charger, in GB they are usually rated at 110V to 240V. IF your charger says this you should have no problem on the 110 Volt American system. The difference in frequency 60Hz USA to 50Hz GB will also not affect your charger.
Tip: If you have a lead with a bathroom shaver socket type head that fits your charger, they are very handy, or, a two pin phone adapter (ex Ericsson in my case) to power my battery charger. Have used in hotels all round the world.
Works for both cam and vidi-cam.
Yes thats a good idea and is what I do but be aware that there are some problems with the two pin shaver plug.
First you need to be sure that the two pin plug is to European Standards and not the older British two pin plug which will not fit all Worldwide two pin sockets. European are longer, thinner and further apart than the British
Secondly much of America uses flat pins - there are some exceptions so you may need to check - so a two round pins plug will not fit.
The adapter I suggested previously will also accept a round two pin plug and adapt it for the flat pins, so if you do have a lead take it (for round pin areas) and the adapter (for flat pin areas.