I think the guys got you covered on the grinders and the info on mixing.
I also suggest mixing by hand. Buy some non-powder filled disposable gloves (if u can find em now) and I suggest getting 1 of these 7inch meat totes/lugs.
www.cabelas.com
Academy also sells them too for a similar price and both places are way less expensive than online vendors.
With only doing 10 pounds at a time you could put the meat cubes/slices in the back half of this tote and then feed the grinder and grind directly into the front end of tote. Most real grinders are made where the grinding plate/spout would fit over the edge of this tote so the meat can fall right into it.
Once all ground you mix up your seasoning slurry in a blender, put on some gloves, and mix by hand.
You could also try using a handheld mixer that has dough hooks or something like that but I hever never done this. Hell a drill with a long enough single cake mixer or dough hook would probably work better but you would have to watch how powerful u run it haha.
Again the meat tote is big enough for you to easily do a hand mix or use a hand mixer in it if u are only doing 10 pounds and will have plenty of room.
If u ever try to upgrade to larger amounts of sausage then I would suggest a minimum of 2 meat totes.
Also you mention u dont want to stuff with the grinder well... stuffers are not very small except the "five" pound stuffer which really only stuffs about 4 pounds a loading.
You can get a vertical 5 pound stuffer as there are a lot of options out there just ensure it has all metal gears. Understand that if u do 10 pounds of grind then a 5 pound stuffer will need to be refilled 3 times to actually stuff 10 pounds of meat since it really only does 4 pounds at a time (4 then 4 then 2 = 10 pounds so 3 loadings).
Knowing this u may wanna start doing 12 pound batches since u gotta fill the stuffer up 3 times any ways and it is really a 4 pound capacity. So u will end up with three loadings of 4 pounds, 4 pounds, and 4 pounds for 12 pounds total. Same effort as doing a 10 pound batch since it is loaded 3 times as well.
I hope this info helps :)