Little confusing trying to decipher your post, so bear with me. It sounds like you have a small inverter hard wired into your cigarette plug and you want to run it through an ignition hot circuit in your fuse panel. I'm sure you could probably find an empty slot in the fuse panel to use, but your best bet is running a fused power source directly from the battery. I'm not sure how many watts your inverter is, but the thin wire typically used for the fuse panel is not the best to run an inverter off of.
If you are looking for a much easier way, leave the inverter powered through the cigarette plug and use a relay that is signalled by the ignition switch to allow power to flow to the inverter. That way your not relying on the ignition for power, and you won't have as much wiring to do.