Clear Silicone instead of Plumbers Putty

The short answer is, no. It won't work, or not for long. There must be a hardware store closer than that, they have plumbers putty. I assume you have tried tightening the disposal clamp screws underneath??? You need to remove the disposal, throughly clean around the hole and reinstall with new putty. It doesn't take long and should fix the problem. If the disposal clamp is rusted, replacements are available at big box and some hardware stores.