Fit is very important .The alloys flow through the joint by capillary action! Strength is also dependant on fit .Ideally the clearance should be .003" for best capillary flow and for strength. Take the time to fit it correctly.
Eutectic type solders go directly from solid to liquid without any 'mushy' stage.Cadmium solders are as toxic as lead solders.To solder stainless steel use 96Sn4Ag and use a flux designed for stainless.This type of solder is also food safe so use it to fix your wife's pots !!