I use over the counter PineOil based cleaners u can get in craft stores or online, of course. Windsor Newton makes a fair one, just use it outside, phewww....
I won't claim its conservation work, in fact, i'm sure its far from it. But i tell the customer that right up front that this is not a conservation process and for those that show any hint of concern i will redirect them to seek a conservator and bring it back for framing.
Most customers however, arent looking for awesome, they're just looking for clean. That said, i will only take the job with a waiver stating they know it isnt a conservation process and that it may damage the art.
I will always test the mixture on the edges first and brave a corner with a q-tip. i let it dry a few days before reapproaching the picture and if the tests go well, i will progress into background. If all goes well, i will lightly do the main focus of the painting.
So far, its all gone well. I've used it on 100 year old canvas all the way down to a painting on chipboard and so far no ill effects.
Good luck.