Monti, I use 50/50 BLO and mineral spirits a lot. Dunking is easier than applying with a brush. I bought a cheap metal oven dish a couple of inches deep and put my work-piece in that. I pour over the BLO mix trying to cover all the nooks and crannies and then turn the work over and check from the other side. Once I am happy and it has had a few minutes, I hang it to dry over the dish. When it has stopped dripping I pour the mix back into a jam jar with a lid and keep it for the next job. I also hang the tray over the jar with a funnel to get as much as I can off the tray. You can clean the tray with mineral spirits if you like too. If I use rags or paper towels at all, I soak them in water and dispose of them in an outside bin. I am very careful about that and have not had any problems.
If I were you, I would test on a piece of scrap from the work you cut first so you can be sure you will like the result before committing yourself.
Rob