By: "Shim," I assume you mean Shimano.
By: "Breaks," I assume you mean brakes.
If I have the correct understanding:
Cantilever brakes have the same pull ratio as road brake levers as road disc brakes...So yes, all your parts road Shimano 105, road disc brakes, cantilever brakes, road caliper brakes are compatible & will work together.
Shimano BR-CT91 are about $14. For the rear, this is a given.
For the front, since you have the option, I like TRP Spyre. But another BR-CT91 would work. Pick according to your wheel.
Where you run into issues is with linear pull v-brakes, mountain disc brakes & road brake levers. Not enough lever travel to to make pads contact & still have enough to actually brake with. Or vice/versa with road brakes & mountain levers. Super firm brake & not enough leverage to effect a stop.
Neither is your case.
Install & have fun.
Last edited by base2; 04-15-20 at 10:15 PM.