I have successfully washed wool tapestries, but they have never been anywhere near the age of yours! I think you need to decide whether you are prepared to lose it if it all goes wrong. If so, you could try washing it in something gentle, like Dreft (is that even made any more?) Dunk it gently in the water, don’t rub, just keep gently dunking)). Depending on how grubby it is, you may need to repeat this a couple of times. Then rinse gently in tepid water. Very gently squeeze out as much excess water as possible. Place it upside down onto a hand towel onto a hard surface, and gently ease it into shape, then dab it to get a bit more water off. (Pressing it onto the towel means you don’t flatten your stitches, and putting it upside down means you press from the back, again protecting your stitches). Then, cover with an ironing cloth (these are invaluable if you are going to make a habit of stitching) and press with a iron on a low temperature. Do not iron in the normal way, just iron by pressing the iron gently onto each part of the work in turn. Hang over a towel rail or similar to continue drying.
Good luck, because, as I said, the age of the fabric might mean it disintegrates as soon as it hits the water.