Replacing a stem is not all that hard, depending on where the stem
has broken. If it has broken at the crown you will have to replace
both stem and crown, if it is just the stem that is broken it’s
easier. Does the movement have a number?, are stems easily available?,
would a stem extension fit? If it has a movement number, your local
horological supplier should be able to help locate a stem or supply
you with an appropriate extension. Then its just a matter of cutting
the stem to length with a snips, and then use a stone to tidy up the
cut end, leaving the threads even as to avoid damaging the threads in
the crown when fitting. When replacing the stem it is important to get
the length right, as to avoid the crown sticking out too far as a
result of leaving it too long , or, leaving the clutch in the hand
setting position as a result of leaving it too short. It’s then just a
matter of trial and error to get the right length. Remember it’s
easier to leave the stem long and have to stone off a bit more, but if
you do cut it too short you can always pack the crown with a tiny
piece of paper, this reduces the depth of the hole in the crown an
thus adds to the crown/stem length.
As for the water resistant crown, just how water resistant is a cheep
watch? There is a big difference between water resistant and
waterproof. An ordinary crown would probably do if you are unable to
reuse the original.
Hope this is a help, Neil KilBane , Longford, Ireland.