Is there a way to use TOR Browser (modified version of Firefox) but without using the TOR network? I'd take to use it for all by browsing activity as it includes a lot of fingerprinting countermeasures.
By definition no. The core of TOR is that by bouncing through the network you become less identifiable the extra tools just reduce the remaining possible identifiers. You could install NoScript as an extension to your normal browser but to my knowledge that's about as far as you can go without using the network.
If you want to avoid leaving fingerprints rent a vpn, remote access it, and then browse the internet via any browser on the vpn, your IP will be the only -direct- trace... that and whatever you use to register the vpn... and whatever the vpn provider uses to canvas the systems to prove you're not a bot... so... yeah there's that. -edit- I do realize the inherit flaws with this choice, it is a valid option I've seen suggested so many times which is why I followed it with the logical faults with this "option"