I have done it on my mountain bike many times. I use a syringe with hipodermic needle. Use some soapy water -with dishwashing liquid-. Remove the switches and pump the water from that side. Not much will go in, so twist the grips until they accept more. A little heat from a hairdrier goes a long way too, as it softens the rubber and plastic. I also use a screwdriver to put it in so I make room for the water, that once inside makes his way. I don't care about scratching the bars with the screwdriver because there will always be a grip over it.
Raul