Okay, I know the noise is related to mating but I'm wondering is it possible that not being with the girls could be causing him actual pain?
No, just frustrated.

He'll get over it.

When I started this thread two weeks ago, Buddy was making horrible squealing noises that I've only heard in times of pain. Annie was sniffing at him through her cage bars and he was going mad trying to get in to her. He was fine the next day and has been for two weeks.
When this happens, I would move him to another room. BTW
How close are the cages? Tonight, I let the girls out in the hall for play and Pixie did a wee on the carpet. She does this every few weeks and Buddy usually goes mental bouncing around and making little mating squeaks if he smells it so I guess she does that when she's in heat??
Probably.
*Do you know how to tell if one of the girls are in season?
* Tonight, I let him out in the hall after the girls and forgot to clear up the pee first. Once he smelled it, he ran around making these pain squeaking noises. He was wagging his tail and making the mating squeaks too. I've checked him for hair rings and there doesn't seem to be one. Once I put him back in his cage, he stopped making the squeaking noises.
The hopping and swishing of the tail is call the "Swish-swish Tail Dance". This is a way of courting the female. He will do a hop hop swish-swish and get this silly little grin on his face. Males do this from the time a female starts into season until she lets him mate or she goes out of season ... which ever comes first. Punkin, one of our dark tan chins, would do this anytime a female in any of the cages would be in season, we had over 140 females at that time ... Needless to say, the exorcise did not hurt him and he loved to show off for all the females, even if he could not get to them.

I'm booking him in for his operation in the new year and I'm terrified but it's not nice to see him distressed and I think it's be so cruel to let him live his life like that.
If his operation is to neuter him, I would be terrified, too. Chinchillas are very small and are not made exactly like other animals ... neutering is much more invasive for the male chinchilla. Chinchillas do not respond well to surgery of any kind. I will not let one of my chins be operated on unless it is a matter of life and death. There are a few ... very few ... exotic vets that are well practiced in this area for male chinchillas.
To better understand some of the sounds, you might want to check out this site ... it's one of the best I've ever been able to find.
http://www.chinchilla-sounds.de/index_en.htm Hope this helps!
Jo Ann
*ADDED: If you notice in the two pictures of the female privates below. In the one that says in season it shows slight swelling and a dot of red blood. This female is in full season. Also, females will tend to clean themselves more often when they are in season.