10mg of propranolol should do the trick 👍 Anxiety's a self-feeding bastard, so if you use propranolol to stop the physical symptoms, it'll starve the anxiety making it weak and vulnerable, leaving your mind totally clear and free to notice the flaws in the overblown thoughts that feed the anxiety from the other side. Then you win
Think of it like a smart, targeted approach to dealing with the problem, rather than the blunt instrument of diazepam.
But if you've been given enough doses of the propranolol to do this, it might be good to try it out in advance — not to see whether it helps with the anxiety, because a) it should and b) you won't be able to tell anyway because in your everyday life you're not experiencing the same kind of anxiety, but because it can sometimes have some side effects that it's good to be aware of in advance (e.g. for me it makes me feel faint when I stand up cause I have crappy blood pressure). It's nice to be aware of how it will make you feel — sometimes people can be initially taken aback by it, because they're not used to their heartbeat being slower, for example.
Don't forget OP's never taken it before; walloping her with 40mg wouldn't exactly be helpful 😆
Incidentally, all this reluctance with benzos is totally unfamiliar to me — I think I must have a facial tattoo that's only visible to doctors that says "Shit, give this one a fuckload of sedatives".
I once went to the OOH at the hospital with anxiety and agitation, where a friend with severe anxiety had been grudgingly given 2 x 2mg diazepam a few weeks earlier, and without even asking for any drugs was given a box of 5mg tablets.
Another time, I was on a 4 x 1mg per day lorazepam dose for two weeks to handle the same thing (anxiety and agitation), was away from home on holiday, and was still anxious, so went to a walk-in centre where they gave me a couple of weeks' worth diazepam at 4 x 5mg per day. Two GPs in the room for some reason, no access to any of my records, but here, have loads of drugs.
I had 28 x 1mg lorazepam on my repeat prescription list until a few months ago — a couple of times my GP asked if I thought we should leave it on there, and when I said I didn't mind either way he just decided to let it stay, and although at my last surgery in a different part of the country I didn't have anything on repeat, all I had to do was go in and ask for something to help with anxiety and they'd give me a load or diazepam or lorazepam :-/
And when they really mean it, they give me clonazepam, but that's only if I'm actually crazy 😂
The only time I've had trouble getting hold of benzos is in hospital, where they'd started me on a drug which essentially switched off my ability to sleep, and people were yelling in distress half the bloody night, and I'd have happily given my big toes for a sleeping tablet 
I don't even really like the stuff, would rather never have to take it, and am perfectly happy to go without it for years at a time… maybe that's why they give it to me. I'd much rather have the propranolol if I could!