I have several tools from the US (brought over with me when I moved), and have never had a problem using a "big yellow box" transformer.
A tip I'd recommend, rather than cutting off the end, just get a good quality short US extension cord (like the ones used for fridges and air conditioner), cut the male end off that and wire in the yellow 110v plug. That way, you keep the tool untouched (nice, if you ever want to get it repaired).
Also, some of the accessories use US plugs and jacks (e.g. my PC pistol grip router base has a US jack into which the router motor plugs). And variable speed (on the PC and several Bosch blue sanders) works fine.
Only one note of theoretical caution: these tools are optimised for the internal fans to cool at 60 cycles per second at a given amount of power flowing through them. When you use a simple yellow transformer, you're now putting through the same amount of power, but the fans are moving slightly slower (relative to 50 cycles per second, rather than 60... a reduction in air movement of ~15%, give or take).
So, same heat generated but 15% less cooling. It just means that the motors of high speed tools (like routers and sanders) get hot quicker. The overheat/overload safeties built into premium tools (DeWalt, Bosch, PC, etc.) should still work fine, though I've yet to have one go off.
It's not a biggie and I've never had any problems, but it's always worth being conscious of your motor's heat.
Hope that helps. -Jim