Yes, you can apply caulk without a caulking gun. If using a tube of caulk, remove from the cardboard or plastic tube-holder, use a puncture tool to get the cartridge flowing, and use your finger to dispense the product where needed. Watch out for drips as this may waste more material than desired. If using a caulking stick, it's best to have a level surface that is clean and dry before you begin applying caulk in either strips or lines if necessary.