Well, if you had to carry a backup gun on your ankle, it would be understandable to carry 2 on each ankle to balance the weight. Being a LEO, it would be understandable for you to have a backup gun. So, no, you're not paranoid.
I personally carry a pepper spray, a Kel-Tec P3AT, a sure-fire flashlight, and no backup gun. I carry the pepper spray because I want to end confrontations in a non-violent manner, if possible. I really don't want to kill anyone. I just want to defend myself. If the bad guy doesn't have a gun, I'll try my best to use the pepper spray first before using my gun. If the bad guy has a gun, then, I'm not fooling around. I'm going to shoot him.
By the way, if you're going to need a back-up gun, keep a rifle in your car. I'd rather have a rifle than a pistol of any caliber, any day. One time, a BG threatened my wife at work and she called the cops. When the cops were about to come, the BG left. After the cops left, the BG came back. So, she called the cops again and the whole ordeal would happen again. Well, the cops quit coming after the 3rd call. They thought that it was a prank caller. So, she called me. I took my AK-47 and put it underneath a trench coat. I escorted her from work to her car and I spotted the BG coming towards us from the other end of the parking lot. I "accidentally" let my AK slip out partially from my trenchcoat. The BG backed off. There are no long gun restrictions in Texas. Thank god! The concealed handgun law wasn't in effect at the time because this was many years ago.
The AK makes a LOUD clak-clak sound when you chamber a round plus the muzzle and banana shaped magazine were sticking out of the trench coat. I had both hands inside the body of the coat holding the gun, the coat was unbuttoned and the sleeves were empty.