Switch to leadership briefly at some point after hunting grizzlies until you have building a fort. After you have building a fort, switch to shooting. Once the money starts rolling in from serving in the army, charlatan, robbing settlers, and especially mercenary work, you can consider respeccing to shooting.
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You don't want to stay pure forever. The only high difficulty trapping job you'll have left that you won't also get with shooting is ambush, which is good, but unnecessary. The only reasons to get high LP in a job are cash and luck, plus being able to change into your dueling gear after the job is scheduled.
Trapping has good money jobs, but shooting is better. Trapping sucks for luck jobs, besides trading with Indians, which isn't at all necessary besides for quests and your time would be better spent on XP jobs, and ambush, will you'll only get by wasting a lot of SP on trapping.