I'd recommend taking it to a watchmaker, likely the crystal comes off (with a crystal tool) and there is a tab that you can see to release the stem, but not having it in front of me, that's a best guess.
Variances in timekeeping, especially speeding up, can also be caused by exposure to magnetic fields, so a quick demagnetization could do the trick as well. Proximity to cellphones will play havoc with vintage watches. The case does protect it to some extent, but the effect can be severe. When I was taking a Rolex course, an unprotected uncased Sub movement was frozen by a cellphone 6 inches away. We had to do some serious demagging as well as re-set the timing machine, which it also badly affected.
It's also possible that the stem is a female one, and will disconnect, but again, I'd recommend letting a watchmaker have a look. I really like the dials on these.