You must have a plan for "just in case". Time is of the essence, not for keeping the fish alive, but a big fish begins to lose weight quickly when stressed and will expell a lot of fluids when they die (even less weight) .If I caught a state record in the waters I normally fish, I know where the nearest place to begin the documentation process (certified scales, witnesses) is and how to get there pronto. Aways have a camera, and nothing beats uninterested witnesses (a fishing buddy is useless as a witness). Always find strangers, and preferably non fishermen to witness THE weighing. I am a Land Surveyor and pull my boat with my work truck, so I have a certified measuring tape I would photograph the fish along side this tape and use it to record girth, etc. Like Cart7 said, you can't work too hard at verifying and documenting.
I have a good live well in my boat. I would leave the fish in the live well and transport her carefully on the boat trailer. I have torrnament weigh in bag (for quick transport to certified scales & witnesses). If you really have a record fish, the odds of the fish surviveing the process of verification is pretty slim, so you just do your best. In your scenerio, if I'm not absoulutlety sure I have a record fish, and I was too, hurried, dumb, lazy or whatever to bring a camera, fish gets released for another day. JMHO
Ronnie