For the OP - I would certainly allow your husband into the anaesthetic room, although as we don't use them at all here (in public or private) he would have to gown up and come into theatre to be with you while you were going off to sleep. Suspect you're in a part of the UK where the anaesthetic room is still used.
However all anaesthetists are different and some are less happy than others to have family in with them. Personally I think if your DH is going to keep you calm I would rather have him there than either you on the ceiling with anxiety or you doped up to the eyeballs on pre-op sedative. I have often suggested to extremely anxious patients (not knowing your history I don't know if this level of anxiety is normal for you) that they bring a relative or friend with them at least to the ante-room.
For the procedure you've mentioned I wouldn't intubate unless you were significantly overweight or had very bad gastric acid/reflux problems - an LMA would be fine (or even a facemask, depends on how fast the surgeon is). You can still get a sore throat with an LMA though, but it should ease after a drink.
To be considering cancelling surgery without your husband present is not a normal level of anxiety which suggests there is a whole backstory here of which I am obviously unaware (and don't really need to know). Just the fact that you are considering it means (imho) there is justification in allowing your request.
Regarding the regional vs general debate raised above - unless you have a (very rare and inherited) severe reaction to general anaesthetics, I would say a GA is safer. The risks are minimal if you are generally healthy, the anaesthetic lasts as long as surgery does (5mins before to 5mins after) and you are awake, able to eat/drink/go home much sooner. With a spinal you are likely to be immobile for at least 2h (if not longer) waiting for the block to wear off again (bearing in mind the procedure lasts 15mins), there may be problems passing urine in the first hour or 2 post op relating to either the drugs in the spinal fluid or the lack of sensation which will delay your discharge - and more to the point, you'll be awake all the way through the procedure. Which I suspect is not what you would want or need. There are also other risks involved with a spinal which, although rare, should be considered (headache, nerve injury and failure being the big 3).
Spinal anaesthetic is perfect for the older gentleman undergoing urological surgery for a variety of different reasons which aren't relevant here. It's also perfect for elective caesarean sections as it doesn't affect the baby and the mother gets to be awake during the birth.
Long answer cut short - I don't think you're being unreasonable at all, I hope your anaesthetist agrees!