Laser weld? Cheap?
I don't think so Tim
The only laser welders I know of are all CNC controlled and take ages to set up, they're not for one offs
I may be out of touch but I haven't heard of any hand held laser cutting or welding torchs as they require sending the beam via mirrors.
If the splines are stripped then I wouldn't bother welding it, welds don't like situations like this when there is torsional stress and the hit home on the return won't do it any favours either, this is why Yamaha designed it with the splines to take the load.
If the splines still hold then a weld would be fine to stop the part moving sideways on the shaft