I mainly Camera Op, but can also edit and started off in a similar way to the way you're intending, but I'd had a bit more camera operating experience and so really the editing came after, which is why I was giving you an answer from the perspective of all round video production.
Having said that, as you describe it, you may be OK starting slowly, offering editing services as a way in. It's just that folk may ask you to shoot some stuff as well, so it would be crazy not to learn camera techniques just in case.
Starting off small by perhaps doing a couple of projects cheaply for friends/relatives/neighbours and things may snowball by word of mouth. As you get more experienced, you may be able to advertise locally or on the web. You just don't want to promise what you can't deliver and get negative feedback.
If you're not too experienced, don't put all your eggs in one basket and invest all you have and chuck in your job.
I went back to college as a mature student and took a college degree in Media Production, with tutors that had TV, Film and Radio Industry experience. I also did as much as I could out of college to increase my knowledge and scrimped and saved for equipment a bit at a time.
After college I worked in a crappy job part time, doing bits and pieces, both for myself and for others who'd seen I was serious and reliable and knew how to wield a camera in a half decent fashion.
As I got more work, it put me in a position to be able to chuck in my old job, but I didn't do it 'till I was sure I could get enough work to pay the bills. I've done corporates, weddings, music video, documentary, fiction and freelance news camera, mostly camera op but also editing, sound, directing - it helps to be able to multitask!
So my advice is to start it off as a sideline, learn as much as you can and only upgrade your equipment if you can justify the expense or need. You may start editing home videos for people but as your capabilities expand, different avenues may open. It really does depend upon how much you want it and how much you're prepared to put in.
Either that or win the lottery or marry a rich widow!
Good luck.
D.