One thing I've found helpful in preventing solder "overflow" stuck onto the blade or front of my brass bolsters (on chef knives) is to 'mask' the areas where you don't want solder. The logic: if, to get solder to stick, the surfaces must be clean -- well, then, if they're not clean it shouldn't stick, right? Research turned up using (a) a paste of yellow ochre or red jewelers' rouge powders (both iron oxides), and (b) welders' soapstone stick. So far I found soapstone to work pretty well; yellow ochre not as much; haven't tried rouge.
That said, seems pretty smart to try hard to avoid having too much solder in the first place - no excess, no spillover. I've had good results with a tip from the 4-part BoseKnives vids on YouTube: tinning the bolsters in advance. Clean & flux the mating surfaces, heat 'em up, apply some solder to get an even thin coating. (Bose does a practiced 'fling' to get excess off; I've got mine in a vise so I've used a piece of 1/16" brass rod to kind of wipe it off if I overapply the solder.) Then re-clean everything; pin, peen, and/or clamp it all together; and heat it up (again, slowly!). Put wee bits onto the joints so you can see the flow point happen and to fill any gaps at the edges. I'd also recommend positioning it so any overflow runs down onto the tang or spine/belly - those you can sand/file off and clean up, vs. at the base of the blade where it meets the bolster (DAMHIKT).
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Hard Le$$on$ You Can Avoid Learning Your$elf: silver solder (I use Harris Stay-Brite w/ Stay-Clean flux) seems almost perfectly engineered to be impossible to remove excess cleanly other than with brute grinding - it's somehow both gummy and hard as hell. After just the obvious small needle files (cf: "gummy"), I've tried rubber abrasive grinding points, diamond riffle files, tiny strips of ceramic abrasive paper glued around popsicle-stick edges, heating the area and trying to suck it up with copper de-soldering wick - you name it. Generally I've come to the conclusion that it's not worth it "chasing a mistake down the rabbit hole"* Better to just scrap the bolster (e.g. bandsaw it off; grind remnants off; touch-up the blade surface; re-drill the pin holes, etc.) and re-do with a new one -- or just scrap the whole blade and move on to the next.
* my term for the trap of trying to fix something, then fix the fix, then fix that, then swear a lot, etc., instead of just being smart by accepting reality, cutting losses, and backing up, at the beginning.