There are many guides available so it's very much possible if get good weather and if you can tolerate the altitude sickness. You'll probably be out of breath so I don't know if it's much fun.
I'm thinking of a few days in the Javakheti Plateau beforehand, may get up to 3000m, so that should help with acclimatisation.
You can book a guide through Internet. We were in Mestia couple of weeks ago and we met Idris Khergiani there. He speaks good English and he's done Kasbegh over 50 times.
I don't know about prices but I suppose you can Google them or email him directly at email@example.com.
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