If you are going to go that far into it, you might as well crack the transmission open and get that old oil out of there which is probably dragging its speed down. Also, replace the lower o-ring that WILL leak, if it isn't leaking already (I'm sure its). You'll need a pick set it remove and install the o-ring. It's up to you if you want to replace other parts since they're getting hard to find. When I crack a trans open, I replace the Delrin pinion gear, both clutch washers, and the lower o-ring. I also disassemble the upper trans housing but I would not recommend doing that since it's very involved and getting the groove pin out is a royal PITA. The groove pin is almost impossible to find now. Just flush the upper housing out the best you can through orifice in the housing.
I'd also add the older A4298 seal and install it under the triple lip seal as insurance.
The transmission top gasket is impossible to find now but you can use a good quality Permatex gasket sealer as a replacement. I used Toyota FIPG on my daily driver almost 15 years ago when the new trans gasket fell into the new oil and I didn't want to order and wait for another gasket to arrive. Still 100% leak free.
As far as the pump goes, Zoomspout turbine oil is the only oil that will pour through the very tiny orifice. You won't be able get a thicker non detergent/non paraffin oil in there such as the blue can of 3 in 1 without making a total mess of things.
Not sure I'd put that much work into a lowly 106 but if you're happy with the machine and want to keep it forever, it's worth the effort. It's definitely a good machine to start out with and learn on, making mistakes along the way. Then you can use your newfound knowledge on nice, higher end machines without fear of messing up/destroying them.