My experience is that the hospitals are hopeless & don't undertsand what no insulin does to a diabetic. I had keyhole surgery on my shuolder three years ago. I was told that I'd be first on the list for the day as they wouldn't want to keep me hanging around with no insulin/food. I was told to have nothing to eat or drink after 22:00 and no insulin in the morning (at that time I was on a morning/evening levemir along with my rapid acting humalog at mealtimes). I also suffered from serious dawn phenomenom so always woke up in double figures and used my breakfast bolus dose to bring my BG down.
I tested before I went to the hospital my BG was about 11 (normal on waking for those days). I was admitted & then left to my own devices for hours, having been told that I was second on the list after all. At 10:30 I tested again & was at 18 and rising!! I went to the nurses station & asked what was going on, told them that my BG was getting silly high & something needed to be done. Only then did they go into a major panic & hook me up to an insulin drip. All because no one really knew what to do with a diabetic patient!! My op was cancelled that day & I had to go through it again two weeks later, but at least the second time I was first in so my BGs didn't have the chance to get to silly levels.
I think that if your op isn't until the afternoon and if you only take one basal insulin in the evening, you should be OK with this dose the night before (I assume that you're on Lantus?). The hospital didn't take my insulin pens from me when I was admitted (and I didn't offer them up either!), so I was able to have my injections as normal once I'd come around. I'd do the same if I was you.
If you're having knee surgery, I assume that you'll be on an orthapedic ward so assume that the nurses have no knowledge of diabetes (except maybe type 2s as my ward was full of pensioners having hip replacements). You'll need to keep control of your own diabetes & don't be afraid to make a noise if they ignore you when you're 'nil by mouth', do your own tests if they don't bother & tell the sister if your BGs are rising. Take glucose/hypo remedy with you so you don't have to ask for it if needs be.
If you eat before 06:00 and have your normal short-acting bolus insulin, this will have passed out of your system long before you go off to the hospital. there's no way you'll be hypo if you bolus half your dose then eat. Were you thinking of bolusing half your dose & not eating? That sounds risky. I'd just get up early and eat/bolus as normal before the cut off time (though the odd half hour won't hurt if you eat at 06:00 or 06:15.)
After my op (I was in surgery about 90 mins I think) I was hooked up to an insulin drip for a couple of hours until I was awake and drinking normally. They tested my blood sugar every two hours all day after the op, so things were better then.
I am vegetarian & all they could offer me to eat for lunch, then dinner & the following lunch was jacket potatoes!! This was despite me telling them before I came in & being assured that there'd be something suitable on the trolley. Again, the ignorance was surprising, they just didn't realise that jacket potatoes are not a good food for a diabetic, neither did they seem to care. Eventually it was the cleaner who went down to the canteen & obtained a proper meal for me after she heard me tell the food trolley person that I did not want to eat a jacket potato for the third time and that they should have something else for me by now.
Good luck. I was amazed how good keyhole surgery is, I was moving my arm after three days & the scars are almost invisible after three years.