That crankcase probably won't hold a cup of mix. I have filled them up with mix and poured it back out a couple of times. A spray can of 2-26 with the case upside down will get that water out as well, what it's made for.
I take my finger and rub 2 cycle oil in the cylinder when I put it back together. I have used moly grease on my finger.
Never seen it make one bit of difference.
Is a spray going to get inside the lower end bearings completely? And rinse it out completely?
I used to teach organic chemistry, I know many ways to get rid of water. Rinsing with alcohol is one of the best, and inexpensive. I always have a stock of dry gas for my 4-stroke engines handy.
A can of isopropyl dry gas (better than methanol, it mixes better with pre-mix) will rinse the case completely several times. You can even turn the crank a few times with the case full. Do that before the mix, slosh it around then let it drain between each rinse
If you want to get a light coating of oil inside the case, and flush out more crud, yes a cup of mix. 3 whole cup fulls won't cost you a $1. You won't leave a pool of oil in the case either. It too will get into every crevice in the case.
If you are going to store it without putting it together, mix up some 10:1 for more residual oil.