The third prong exists to keep you alive.
No, do not use a two-prong adapter. You are removing the ground, which is the only thing that prevents the metal case of a tool or appliance from shocking you.
The third prong is the ground wire. If a hot wire inside your device comes loose and touches the metal casing, the ground gives that electricity a safe path back to the breaker panel instead of through your body. A two-prong adapter breaks that path. The little metal tab on the adapter? That’s meant to be screwed into the outlet’s cover plate screw, which only works if the outlet box itself is grounded – and most old two-prong outlets are not.
If you are in a house with two-prong outlets, either replace the outlet with a GFCI (labeled “No Equipment Ground”) or use a proper three-prong extension cord running from a grounded outlet elsewhere. Don’t fool yourself into thinking the adapter is fine. It’s fine until it isn’t.