as a blocking issue could make the machine inaccessible

Not really, the password command will not update the passwords database until the interactive dialog finishes, so the worst thing that can happen is ending with an unchanged password.

Anyway, check also IPC::PerlSSH. Its documentation says that it allows to transfer and run Perl modules, scripts or code on the remote machine without installed anything there.

Another option, would be to make, anyhow, sshfs work over an SSH channel in the reverse direction (mounting a client share into the server). Update: I have added that feature to Net::OpenSSH but it is highly experimental, and requires a patched version of sshfs. It is available from the GitHub repository on the sshfs branch.