Toddsndrsn,
Jim Kibler has posted a video about this.
Jim's technique doesn't involve welding, but then again, in the repair he is making the whole is not so close to the edge as is yours there.
On a side note, the normal way to avoid this is to determine your optimum position for the bolt to pass in the lock bolster, drill that hole first, and then with the lock in the mortise use that hole to guide the drill. The hole in the wood is then enlarged later.
To be sure the hole goes straight through where you need it to go, it's helpful to also figure out exactly where you want it to come out on the side plate side, then drill so that the two points align. If you have a drill press, this can be done with a simple alignment pin jig in a shallow starter hole on the bottom side. If you are doing it with a hand drill, then it can be done by drilling with a slightly undersized bit, drilling just past 1/2 way from each side, then connect the two holes by drilling through to get them aligned. Then enlarge.
Of course you are going to need to put a dowel in the stock to repair the hole that was misaligned. Wood glue is fine.