I've silver soldered (hard solder) extensions to sear arms that are too short on alot of guns,,mostly SxS shotguns and they've worked out just fine.
Use a simple lap joint to give it a bit of extra strength. Hold the nose of the sear right in the vise jaw to act as a heat sink. Set everything else up with flux, part wired or clamped and ready to go.
Quick heat w/a torch (I use acetylene) and a touch of the silver solder wire to the joint and it's done.
Let it cool, file it to shape and length.
Welding is easier if you have the equiptment to put a little bit on the end of the arm w/o burning through it.
I just find silver soldering easier for such things.
Slipping a piece of close fitting but small dia tubeing over the arm is decent fix too and can be soft soldered instead. Make sure there is enough room below the level of the original arm for the trigger to still function with the new extension in place as it'll sit lower (and higher) when in place.
Several different ways to do it.
On the long tanged sears of most SxS (cartridge) shotguns, many are mangled with plier marks and simply bent inwards to catch the trigger blade. Hardly workmanlike and on a sidelock, you usually don't have a sear w/a tang that long anyway.