Why not do it yourself? Tons of videos on youtube on "how to". Books are out there.
My goto book Basic Butchering of Livestock & Game by John J Mettler jr
always in my hunting kit
costs are low , $40 for butcher paper roll that will last many seasons, I'm sure you have knifes so nothing.
I can understand if space is an issue but if you have somewhere to butcher it is a good skill to learn. In just two seasons my skill as wells my friend
improved from a bloody mess to very presentable cuts, ( no book first year we just followed the muscles). It's very satisfying to take game from field to table.
Moving forward we have bought more stuff, meat grinder, sausage machine etc but basic stuff the cost is minimal way less than one deer being done at butcher.
My other buddy take his butcher and has it done, he always seem to be scrambling, making phone calls etc. We are chill, hang the deer a day or two then get to butchering.
We have a few beers and a good time , no stress.
Just some food for thought. All the best.