My carry revolvers are J, K L and N Frame size handguns with barrels from 2" thru 4". I carry my 4" 64 some, same size as your Model 10. I carry it in a Lobo Enhanced Pancake at 4 O'Clock, like everything else.
With a barrel over 2-1/2" at 4 O'Clock you cannot access your Billfold in your right rear pocket. I move my billfold to a different pocket. In slacks that is normally my Left front pocket.
For shirts I have a big selection of Flowerdy Shirts, Fishing Shirts, Woolrich Discrete Carry Shirts, and others that are sized correctly for concealed carry.
I have 7 or 8 fishing shirts. I have been wearing them almost daily during the week over a white Tee shirt the last month.
Once you get the shirts worked out, work on the Model 10 grips. I would do some looking for a set of wood grips that are nice and round on the butt end, if you do not have a good set on the gun now. The shirts slide around wood grips without sticking.
You can carry the 4" K Frame without any serious issues. You might keep an eye out for a 3" Round Butt 64 or 65. They are still a very Shootable Platform, only easier to conceal. I carry my 2-1/2" 66 all the time.
The good point about a K Frame is the ability to get rounds on target with one. They are a very User Friendly handgun, and they are very Shootable.
A J Frame is easier to conceal, but also much harder to hit with.
Bob