It really depends on what your betta died from.. the only symptom was swollen gills? That's either parasites or water issues.
More info might help determine which: http://www.bettafish.com/showthread.php?t=49233
But basically, to be the most safe, I would not house the snails with any bettas. The tank I would toss everything porous (gravel, ornaments, filter media, etc) and bleach everything else inside the tank (filter itself, thermometer, heater) in 10% bleach solution for 10-15 minutes. Then rinse everything like crazy until there is no bleach smell at all. Then refill everything once more and add a super dose of conditioner, and let that soak Then rinse everything once more and let sit out dry 24 hours before you add anything new.