IMO it'd be relatively easier to do the glass cockpit mod than the sidestick. You couldn't just move the stick to the right, make the required mechanical changes, and say Bob's Your Uncle. A SSC almost guarantees a conversion to FBW, so you'd have to completely redesign the FCS. Add an all-flying tail (no elevators or tabs). Run new plumbing and wiring and a hydraulic power source of at least 2000 psi to have any kind of surface authority. Then there's hardware to design, code to write, a testing regime to undergo, flight tests, yadda yadda yadda.... If it flies well already (and I'm sure it does), it's just not worth all that hassle just to have the stick on the side.
Light enough? Probably. It obviously works on the SR-22. But to get military style performance from a mechanical SSC, you'll almost certainly need at least some rudimentary assist. Hydraulically driven surfaces comes to mind. Move a pushrod, open/close a valve connected to the surface. The L-39 already has a hydraulic system for flaps, gear, speed brakes, etc. Is there enough pressure to drive the surfaces? And what would you do in the case of hydraulic failure? Mechanical reversion? My point is you're adding a level of complexity to an FCS that already works pretty well given the platform (it can do +8/-4g thank ya kindly) for a small amount of convenience and elbow room.