Winches are modern miracles of science that are engineered to give you leverage on your lines. They are not savage beasts. We made them and we are their masters.
That said, what brand of winches are they? That might help in finding a web resource you could use to DIY. I have found maintenance manuals for Lewmar winches on the web for instance.
I consider myself moderately handy but confidence comes with doing the proper research and having the right tools and approach.
If you are unsure you should get a cardboard box about 1' square that you can cut a hole in the bottom of to fit over the winch. This is to help catch any parts that want to fly off the assembly and overboard. Make the hole large enough to tape it down around the winch.
Once you find the 'key' to dismantling your winch (the Lewmar uses a stopper fitting that is shaped like a round "C" IIRC Lewmar
) the rest is pretty easy. Photograph the dismantling process if you are really unsure of how to put it back together (also examine the exploded winch picture on the Lewmar website I already linked to have an idea what to expect to find inside. Print this if you need to.).
Basically you want to clean and re-lube the winch. Wipe down the parts that have any dirt, grime or grease on them (soaking in mineral spirits would work too).
Based on the Lewmar winches the only springs that can really fly off the thing are behind the 'pawls', the things that catch on the winch body to keep it from spinning freely in a backwards direction. The 'pawls' have springs behind them that push them out so they catch the winch body (sometimes these need to be replaced although I have never done this).
Read the details specified by the Lewmar website I have already linked that tell you how to re-lubricate the various components of the winch. Do not use any grease on the 'pawls' as this may make them sticky and inoperative.
There may be winches with a different kind of inner-workings but I really doubt it. Why re-invent the wheel. Most winches I have dealt with have a different 'key' to opening them up.
If you have the 'yard' do this for you I would think you might pay over $100 dollars for what is essentially about 3/4 hours worth of work (loser). If you do it yourself you will gain both financially and in your own confidence level.