Well, I would imagine that unless you get serious advice from someone who's skilled at roofing, you could end up with worse leaks than you have now. It's not something you want to chance, after all.

I would say that the level of difficulty depends completely on your knowledge of what the job requires and your ability to do the work on a sloping roof.
1. If you lay something down on the roof and it slides off to the ground then the roof is probably too steep for an amateur to be working on.
2. Ripping the old skylight out is the relatively easy part, just don't tear up any of the adjoining roof or you will have to repair that also.
3. Covering the resulting hole with sheeting is pretty straight forward just make sure it is supported underneath by 2x4's all around the hole . Use at least the same thickness of sheeting that is on the existing roof.
4. You will have to carefully lift up the shingles and slide felt (tar paper)under them at least one foot all around, more would be better.
5. Depending on the age of your roof matching the new shingles to the old may not be possible as far as color goes. You have to weave the new shingles into the old ones.

If all that sounds easy enough to you then go for it, otherwise have some one that knows to do it, do the job

Ask the roofer for a price. If it's easy enough for you to do, the price can't be much.

The problem is finding a roofer willing to take on a small job. Best bet might be to find some that are working the neighborhood and then maybe... Otherwise, on little jobs like this, you're pretty much stuck with doing it yourself.

You don't give any hint as to you're abilities, so who knows if you could do it. You don't say how big the skylights are, so who knows if the price point is decent for the work.
Get other estimates, maybe you can keep the openings.
Ron