Not a test, per se, but some of those pertinent qualities are listed here: [Reference] Physical and Mechanical Properties of Solder Alloys
I’m in agreement about source of irritation being the flux rather than the lead. Active fume reduction/movement is pretty much standard at pro benches and you can get decent cheaper units these days for $45 to $80 without going all in on a commercial unit ($$:money_mouth_face:. It’s been a long time since I’ve done enough soldering for a length of time to really bother me, but it used to get me a little with sinuses and a headache…most of that was acid core and non-electronics rosin core, though.