Making TB Portable default mail client without changing Windows 10 registry

I am using TB Portable (60.9.0) on a computer that runs Windows 10.
The main reason I use a portable version is that I don't have admin privileges to install any software on the machine.

I would like to set Thunderbird as default mail client (i.e. when clicking email links I would like to directly use Thunderbird for composing a new message).

Unfortunately all solutions that I found here and more in general online suggest to: (1) install a non-portable Thunderbird version, so that that can be set as default mail client; or (2) change the Windows registry.

Neither of these work for me because I don't have privileges to modify the registry in any way.
Moreover, these seem to me pretty sub-optimal workarounds:
at least in Windows, one of the (really) big advantages of using portable apps is precisely that we don't have to modify the registry...

Is there a way to accomplish what I would like to do? (perhaps from the bat file that I use to start TB while specifying the profile to use?)

Many thanks,
S.