Are you planning to put the shifters on the flat section near the stem, or out on the horns?
If by the stem, some Paul's thumbies and a suitable pair of bar end shifters should sort out shifting for you.
Don't think thumb shifters would line up well out on the horns.
If your bike came with linear brakes, it probably has fairly good clearance. Means you'll need long-reach caliper brakes.
Expect to lose a fair amount of brake performance.

I'd prefer to try bar end shifters in their regular position either together with JTEK Aerobrake Jtek Engineering AeroBrake bar end shifter mounted brake lever
Or bar end shifters together with cross/interrupter levers mounted in reverse.