The CDC states- "You will not get Lyme disease from eating venison or squirrel meat, but in keeping with general food safety principles, always cook meat thoroughly. Note that hunting and dressing deer or squirrels may bring you into close contact with infected ticks." Source
Since there are no studies on which they base their assumptions and their history of being correct about any aspect of Lyme disease is dismal at best, until there are studies indicating that it is not possible to contract Lyme or other tick borne diseaes from wild game, please use any precautions you feel are necessary to protect yourself and your family.
NOTE- Wild mammals and birds are often asymptomatic reservoirs for the bacteria and they rarely become ill.
QUOTE- "A 25-year-old Royal Marine was evacuated to the Royal Centre for Defence Medicine in Birmingham, UK, with a history of rash consistent with erythema chronicum migrans, a seizure, and lymphocytic pleocytosis after skinning reindeer in Norway." Source
QUOTE- "Our results indicate that a high number of animal species in the Czech zoos were exposed to Bb s.l. and that TBEV infection occurred at least in one of the investigated zoos." Source