When I installed my heated grips I think that I put another wire which was easier to feed into the handlebars in first and tied it to the heated grip wires to pull them through. I think that I may have used a small hook as well.
It's Friday afternoon and my memory is fuzzy.
If you are having trouble getting the old grips off then try sliding a thin flat blade screwdriver in under them, squirting some WD40 in under them, and twisting them off. Clean the bars well before putting the new grips on.