If you get your male fixed, you need to insure that you have a GOOD vet who is willing to do it. There is a thread in the "Vet Questions" regarding how our resident "go-to" vet fixes chinchillas and I'm sure she'd be willing to answer any questions another vet would have regarding the procedure. The price is going to vary by area though, so you'd have to ask your vet what he or she would charge.
There are quite a few people who have had their males fixed with no problems. However, you are going to need to keep him apart from mom for at least 30 days to insure all viable semen has died and so he has time to heal.
But you need to separate NOW so that if she's not already pregnant, she doesn't become pregnant. You can also separate now and wait to see what she has if she is pregnant. If she has a male and a female kit, you can pair the female with mom and the male with dad when old enough. Each half of the FF cage is plenty big enough for 2 chinchillas if the situation turns out that way.