Your spouse should talk to the gemeinde office or the cantonal migrationsamt. Usually a dependent permit is renewed along with the primary permit. If they cooperate, then you might be issued a visa by the Swiss embassy in India quickly.
Ultimately the Swiss consulates will follow the directive of the Federal Office for Migration. They can be contacted at: https://www.bfm.admin.ch/bfm/en/home...s/kontakt.html
In my experience, they provide good information.
IMHO, coming here on a tourist visa not a good idea. It might just prolong the time it needs to get the permit again, and also break the continuity of your residency here. And you might have to leave Switzerland, get a entry visa for long stay stamped, and then come back.