How to replace handles?
The rubber degrades and goes super tacky and gross as you note. The rubber and plastic part does remove by pulling outwards - and could therefore be replaced - this is how you change cables on these SRAM gripshift. The problem however is that the rubber rotating part is probably not available as a spare part. The shifter unit itself is generally considered cheap enough as a whole.
Searching online for 'SRAM rotating grip assembly' does bring up some spare parts, though I can't see a straight match and they are about the same cost as a whole replacement unit. These seem to be for higher tier units.
A visit to your local SRAM Dealer might be helpful, they could look up the current spare parts catalogue with you and see if it's even listed as a spare, more categorically.
Bear in mind that replacement units come with their own inner cable, so it might be a reasonable time to go with new units and saving the cost of the inner cable as a nice part to freshen up too.