Update: After further discussions on the CB, it turns out that the OP wants to set the first option to the first alphanumeric value.

What follows is an explanation of what the original code is doing.

You probably want:

$mech->set_visible([ option => qr/.+/ ]);
#                              ^^
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What you have is the same as:

$mech->set_visible([ option => ($_ =~ m/.+/) ]);
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In other words, you are passing the result of matching qr/.+/ against $_ (and this likely is where the Use of uninitialized value warning is coming from), not the regular expression itself.