Galvanic corrosion pops up to mind but is not the only possible explanation. Metals can also make eutectics with a remarkable oxide colour.
"Silver brazing" is not pure silver. Wiki
https://en.wikipedia.org/wiki/Brazing#Silver_brazingtells "such as copper, zinc and cadmium" where Zn and Cd have a potential very far from silver.
Corrosion potentials work... more or less, because some alloys are heterogenous, and other reasons. If your dirt appears in few days without remarkable humidity, it's not necessarily galvanic corrosion.
Corrosion having no excellent theory, I wouldn't stick permanently to the potentials story. This must be experimented anyway.
A different explanation would be that the
brazing flux used to deoxidate the metals is still present and corrodes them. This flux can differ from one solder to an other: boric acid, rosin... and varied alloys react differently to the flux. Then the answer would be instead to brush away all traces of flux, not to cover them with a waterproof layer.
Rosin is rather less aggressive to metals, but it's good practice to brush it away. Boric acid is corrosive and frequently used with silver brazing.
Urethane: I'm not enthusiastic. I once overmolded an electronics circuit in polyurethane foam, and all copper corroded brutally - iron can only go worse. Epoxy may be less aggressive, or maybe glue from a hot glue pistol. If your temperature permits organic coatings, you could consider paints and lacquers, which are designed non-corrosive; car lacquers are hard and waterproof. Or use thermo-shrinking sleeve, if you can let it fit your complex shape: waterproof, chemically inert as a polyolefin.
If you know someone who makes or repairs brass instruments, ask him: they know very well brazing, corrosion and all around it.