is getting rid of skunks a job i can do myself?

Mostly yes, as long as the aim is making your place unappealing rather than catching them. Take away the food: lock bins, bring pet food in, pick up fallen fruit. Then find where it's denning, usually under a deck or shed, and block the entrance after it's left for the night, with mesh buried about a foot down in an L shape so it can't dig under. In spring, be careful you're not sealing young ones in. Trapping is where I'd hand over to a pro - rules on relocating wildlife vary by area.