Fred has a good point. A plain butt weld is inherently weak. Even a simple 45° angle butt weld is stronger.
While most folks don't go as far as make a M&T joint, or have a TIG welder, nearly the same degree of joint strength can be had fairly easily with the simple flux-core wire welders that most folks have.
Tip#1
Do the welding before the blade is shaped beyond the basic profile. Profile the tang about 1/8"-1/4" oversized in width. Cut a "V" where the welded extension will go. Cut a point on the extension piece to tightly fit the "V". Slightly chamfer all edges with a file so there is a small valley running along the weld line. Clamp everything up tight and snug on a flat metal plate and use your wire welder to weld a line down the "V" from one side. Let it cool while clamped, grind that surface flat with your angle grinder ( try and keep clamped), flip the blade over and re-clamp as before, and weld the other side of the "V". Let it cool a bit while clamped and grind the second weld. Remove from the clamps.
Heat the tang to low red once or twice (1000-1200°... still magnetic) and let air cool. Place in the oven at 450F for an hour or two..........Grind the knife as desired. For a narrower hidden tang, the same procedure can be done with a simple 45° joint instead of a "V".
If you want to, a full thermal cycling and speroidization can be done on the blade after the weld and before grinding to remove any hardness or stress. Done right, the weld will be about as strong as the rest of the blade.
As with any welding procedure, practice this on scrap until you know the settings and weld speed needed for getting a full penetration weld. Bend test these practice pieces after annealing and tempering. They may break at or near the weld, but should not snap easily.
Tip #2
At the prices we pay for it, no one likes putting damascus inside a hidden or through tang handle. But do yourself and the knife a favor, if you are going to weld an extension on the damascus, put the joint at least 1-1.5" away from the guard/ricasso. Yes, that is a bit of money to "waste", but if the knife breaks...it is all waste. All the leverage of the blade and handle concentrate in the 1" before and after the handle/blade junction. Is that where you want the weak spot to be in the metal? A wide and strong ricasso, a well fitted guard or bolsters, and a strong and wide section of tang for at least 1" beyond will assure a strong knife. For the same reason, deep choils on either side of the junction are also bad ideas, as the knife will fail at that spot if pushed to the elastic limit.
BTW, that is why they are called "bolsters", as they strengthen the area that is weakest.