You are getting an uninitialized error because you are trying to change the content of $access_num, to which you've assigned $1, but there were no parentheses in your first regular expression. Maybe you mean something like:

if ($line =~ s/^\s*ACCESSION\s*NUMBER:\s*/) {
    $line =~ tr/-//;
}
[download]

or possibly

if ($line =~ s/^\s*ACCESSION\s*NUMBER:\s*([-\d]+)$/m) {
    $access_num = $1; 
    $access_num =~ tr/-//;
}
[download]