I use a homemade jig similar to the one in the video except I use several small clamps. I will take and make the 2 broken ends meet, then put one under the other and slide them together about 3/4" so they overlap. I then clamp the blade down and use a cut off wheel in the 4-1/2" grinder and cut the blade at an angle where the 3 pieces are overlapped. This gives the joint more joining surface helping to make a stronger and longer lasting joint.
Next I put a slight bevel (slight is about all you can do with these thin blades) at the newly cut angled ends..... the top of one, the bottom of the other so when the blade ends are slid together the new bevels meet and the blade is the original thickness.
Next I use a very fine grit sandpaper to clean both sides of the broken ends to about an inch away from the joint. Wipe both ends with common rubbing alcohol or acetone to make sure they are clean. Put a thin coat of silver brazing flux about 3/4" or enough to make sure the whole joint is covered............Fluxes....JW Harris Stay-Silv works good but is a little pricey compared to Oatey Plumbers #5 flux which works with silver and steel as good as the name brand silver fluxes. Also, as in your case, it can be purchased on the weekend at Menards, Farm & Fleet, Ace Hardware when the local welding supply places are closed.......where were we.......clamp the 2 ends together so the bevels mate and the blade is flush at the joint. Add another thin coat of flux to both sides of the joint. Now.....seeing that these blades are fairly thin, you can get by with the type of Mapp torch with the disposable bottles, or you can use your Oxy/Fuel unit. Point a little heat on the top side, then place the heat source below the joint and wait for the flux to bubble and turn somewhat clear. At this point start touching the silver brazing rod or wire to the joint to see if it will start melting. Do not apply direct flame to the rod/wire. Once you have gotten to the point where the rod/wire has melted off a sufficient quantity of silver at the joint, hold the flame still under the blade until you see the silver flow. If capillary action has sucked some of the silver away from the top joint, at this time you can add a little more silver if you flux the rod / wire. Remove heat after you are sure you have a good joint.
Allow blade to cool..............now, it is suggested that a person harden the blade back up since the brazing action annealed it. In the past I have not done this to silver brazed blades because they seem to last a long time as is. If I weld the blades I will temper them because there is no fear that the silver joint will let go. If you are a perfectionist and must harden the brazed blade...........once it has cooled to room temp, heat the blade until it is a dull (very dull for silver) red, then immerse in cold water.
When done with the surgery, use a flap disc or something similar to sand the silver joint down to about flush..don't go crazy here. Just need to make sure the blade will pass through the guide wheels without taking them out or making excessive noise................good luck.