How would you clean this?

Hello again everyone! I'm finally back online, having made the rash decision to up sticks and move to the Isle of Skye. A traumatic experience made worse by our plan to build a house from scratch on a v tight budget - we're both in our 60s, so clearly certifiable! Anyway, one thing to emerge from the carnage is an old oil painting done by my grandfather, which I hadn't seen in a decade! I'll try to attach an image of it. It is about 14" by 10", and done on a Reeves Oil Sketching Tablet. Its value is purely sentimental, but it is in a poor state, almost certainly through hanging in a heavy-smoking environment. I've looked for cleaning advice on the forum, but I'm looking for advice/reassurance before attacking it for real! I don't fancy a preliminary clean with anything water-based as the support seems very absorbent and potentially weak. I'm not sure how to tell if its varnished or not. Much of the surface is "glossy", but there are areas of heavier impasto with a matt appearance, where I guess the top layer has "sunk". Interestingly, the method of mounting has left an "edge" around the painting - some of the paint seems to have stuck to the mount or frame & come away from the support when it was dismantled. I also notice that there is a bead of something (oil? varnish?) forming a sharp line where the mount/frame has been, so I guess it was framed before the paint or varnish was properly dry. To cut to the chase, should I go straight in with some cotton wool & low-odour solvent? Will I be able to tell if its varnish I'm removing or a tarry smoke deposit? Even more pertinently, will it be obvious if the paint itself is being harmed/removed? It must now be very old, so I'm sure no alkyd resins etc would have been used. Thanks in anticipation/trepidation!