The hospital will usually put you on a drip of insulin/glucose mixture. At least they did two years ago. They would not do anything else. My problem with general anaesthetics is not the anaesthetic itself, that is no problem at all, and no more dangerous for us diabetics than for anyone else, but the drip and their management of it. I have heard many stories from many people of great success and no problems, so I know my experiences are not so common, but I have had some doctors refuse to listen to me about the ratios in the drip and every time I've been in hospital for an op they have made me go hypo. So make sure any instructions you give at your pre-op meeting are written down and signed by your consultant, then the ward staff have to obey them.
Having said that I suspect that if you are on a pump they won't even use a drip and will let you manage your fasting period by yourself with your pump. They worry terribly about the BS being high and don't seem to realise that a bit high for a short time is no problem but low for a short time certainly is. One day they will get it through their heads, or maybe the rest of the world has and it's just my hospital. I am in the middle of a serious complaint about it with them.
Now, close your eyes to my scaremongering, talk to your consultant to make sure it all goes as YOU want it and don't let them bully you into doing anything you don't feel right about. You'll be fine. The anaesthetic itself is no problem. And do believe the staff when they say don't eat too much afterwards, because you may not feel sick, but the stomach tends not to cope with proper meals for a bit. I found that out last time.
I had a couple of teeth out by the specialist tooth people and I chose to have it done with a local anaesthetic. I thought it would be difficult, but they are so experienced and have all the right gear that it only took a few minutes and was not the least bit scary or painful. They were wonderful. Much easier than starving for a general. It might be worth considering, unless your op is more serious and needs loads of teeth doing.