My take on this: If your plan is to continue this hobby, try and get a machine or build one yourself and use "proper" liquids. Good ventilation is very important. One option is to make a small cabinet with a (bathroom) fan and a hose:
Pocket watches are (only a bit) easier to work on because of their size, but often need more advanced skills. For instance, they often need a new balance staff or repivoting, have broken teeth, cracked jewels etc. You might be better off starting on wristwatches right away (mens, not ladies).