Cucumbers will germinate from saved seeds. Pick nice fat seeds and dry them off.
You will know the mother but unless you very carefully hand germinate you have to take pot luck as to the father.
Curcurbits can be a bit of fun. You might get something very oddly shaped or something with a very poor taste or something special. Do you mind spending time growing something that might end up a huge waste of effort and space? Seeds produced this way are very cheap and I end up with far to many plants, and little possibility of giving them away since you do not know what you might be giving.
I grow my own runner beans, courgettes and squash, but also grow some standard ones as insurance. Have saved some lemon cucumber for next year. My own beans tolerate my dry growing conditions very well.