I agree with the last statement. Build a replica of your sisters car using the 75 and whatever parts you can from the 77. There isn't much point in transferring the VIN plate if you have the title for the 75. If you did use the 77 VIN plate once you apply for a title it will have your name on it.
You'd be better off to make a plaque with the 77 VIN and title (if you have it -- should still have your sister's name on it?) or a photo of your sister and/or the original car, and a plate saying it's a replica built to honor your sister's memory. The VIN and title won't matter in any case -- no one remembers that the VIN was hers, they remember the car itself. If it looks like her car and people recall it, that's all that matters.
As far as legality... if you own both cars, and you're not doing the swap to circumvent some kind of law (such as emissions -- if 75 is exempt and 77 isn't, you'd have a hard time convincing a cop/judge that wasn't your intent...) or sell a stolen car, I'd do it without saying a word to anyone. Someone has to have reason to complain and bring charges. The only way that might happen is if you're involved in a wreck. The insurance company could claim the car was illegally operated and therefore your policy is invalid. But they would have to know about or have reason to suspect the swap.