I have often heard the "story" that solid state voltage converters can damage a hotel's electrical system, but I'm skeptical. It strikes me as an urban legend.
Can anyone document that story?
By what mechanism can you damage a hotel's electrical system? I think all you can do is to draw too many amps, but the system should have fuses/breakers to prevent that from happening. I once plugged my hair dryer into a "US configuration" receptacle (labeled 120V) next to the sink in a London hotel. The hair dryer started to work and then went dead. There was a breaker box in the room, and I opened it; the tripped breaker was for 10A (about 1200W, too low for the hair dryer). Apparently the receptacle was only intended for shavers.
It is true that the waveform from solid state converters can damage multi-voltage charging systems for computers and phones - or more likely the appliance being charged. Dual voltage hair dryers/curlers/straighteners don't need a converter and should not be damaged nor damage anything (as long as the switch is in the correct position).
If you believe the legend, don't use a USB charger. USB chargers are really voltage converters, 100VAC - 240VAC to 5VDC.
On the other hand, most US hair appliances have safety features that depend on the power source being polarized (their US plug has one blade wider than the other). The power system in most countries is not polarized, so the safety is lost (Switzerland, if you are using a grounding plug adapter, and the UK are possible exceptions), so leave your appliances with polarizing plugs at home.