Given a site can use browser fingerprinting methods, there no tool that would completely cover everything. The paradox is that the more you try to make your browser look like something it isn't, the more unique it becomes. You can use tools like Panopticlick or AmIUnique to investigate your current browser.
Therefore, even with Tor, it's better to use the Tor Browser with its default settings. The Tor Blog has a good article on the subject, Browser Fingerprinting: An Introduction and the Challenges Ahead:
What Makes Fingerprinting A Threat To Online Privacy?
It is pretty simple. First, there is no need to ask for
permissions to collect all this information. Any script running in
your browser can silently build a fingerprint of your device without
you even knowing about it. Second, if one attribute of your browser
fingerprint is unique or if the combination of several attributes is
unique, your device can be identified and tracked online. In that
case, no need for a cookie with an ID in it, the fingerprint is
enough. Hopefully, as we will see in the next sections, a lot of
progress have been made to prevent users from having unique values in
their fingerprint and thus, avoid tracking.
Tor + Fingerprinting
In the end, the approach chosen by Tor developers is simple: all Tor
users should have the exact same fingerprint. No matter what device or
operating system you are using, your browser fingerprint should be the
same as any device running Tor Browser (more details can be found in
the Tor design document).
If you only need two accounts and they shouldn't be linked, it's relatively easy (in theory) to:
- Use different browsers to prevent browser fingerprinting.
- Remember to systematically use a different IP address when using the second account.
- Always close the browser before opening the other to prevent background activity.
However, it's only a matter of time when you do a mistake that could help linking the accounts.