How can I get around a ‘die’ call in a Perl library I can’t modify?

You could wrap it in an eval. See:

perldoc -f eval

For instance, you could write:

# warn if routine calls die
eval { routine_might_die }; warn $@ if $@;

This will turn the fatal error into a warning, which is more or less what you suggested. If die is called, $@ contains the string passed to it.