Hopefully the presta valve stem is removable...many are not...if there are no 'flats' on two sides then it is not likely to be removable.
Slime really doesn't work very well.
Perhaps in this case you will be better served to get a pair of 'tubeless' wheels it they work on your bike. You could even increase puncture protection to tubed or tubeless by using tire liners...they do work well.
There are tires that have more puncture resistant materials in them and they work fairly well, add a tire liner and you may be ok.
They also sell 'thicker' tubes that are supposed to be more puncture resistant.

Good luck and keep us informed...