No need to drain the lower oil unless you are going to replace the oil or seals just place motor on a stand and pull the lower unit off no need to invert engine actually I find it easier not to invert especially when disconecting/ reconnecting the shift linkage. Just tilt it up like on the boat to do the work
I have done it this way on larger motors & it works fine. Depends on how much light you have, You can always get someone to hold a drop light. If the O ring at the power head keeps falling out, just put a dab of grease on it
Suggest you do not remove the driveshaft from the gear case grease. If, when you go to re-install the drive shaft into the power head, & it doesn't want to go in, rotate the lower unit right to left a bit. If that doesn't work turn the motor over SLOWLY with the starter cord, Carful!! The splines on the shaft have to line up with the splines in the power head.
If the new housing doesn't want to slip over the shaft, dress the spot down with some fine sandpaper or steel wool, just enough for the housing to slide down. You may have to do this to get the old housing off. There may be a bit of rust or corrosion on the shaft, making the housing bind a bit. Don't force it.
The most difficult part I encountered was getting the water tube lined up & slid into the O ring in the power head. An extra set of hands & eyes may be helpful. Suggest you get an extra couple of new O rings. If the water tube doesn't want to go in, don't force it, you may damage the O ring & not know it
It wouldn't hurt to put a bit of silicone grease (Plumbers grease), on the impeller vanes before re-installing. Remember (picture) which way the vanes on the old one are facing.