The first is not suitable. ASTM96TS Sn96Ag4 has a melting point of 221–229 °C according to Wikipedia. Pb96Ag4 would be OK, but that is not lead free so doesn't seem to match your description. _Update from comment to explain the letters and numbers: the data comes from wikipedia, the numbers are Tin(Sn) 62%, Pb(Lead) 36%, Ag(Silver) 2%, for example, see below for an electronics solder compound_.
Sn62Pb36Ag2 is an ordinary expensive electronics solder (but not lead free), with an even lower melting point.
You need to find a high temperature silver solder, with a melting point of about 305 °C (which confusingly might be a soft silver solder), for example one of these. Hard silver solders melt at 600 °C, that would be excessive in this application.
The nomenclature 'silver solder' came about before lead-free electronics solder was introduced, since when more alloys containing silver have become popular as general purpose solders.