Good post. Here's what I would do if all I wanted was your last result:

# note the lower-casing inline
($fus = lc $fus) =~ s/\W+/_/g; #all spans of 1 or more non-words becom
+e 1 '_'
$fus =~ s/^_|_$//g;            #at most one on each end, because of th
+e above
[download]

But, for the poster's question, removing all single-quotes and migrating spaces to _...

for ($string) {
   s/\s+/_/g;    #convert 1+ spaces to a single '_'
   s/'|^_|_$//g; #trim lead/trail _ and remove single quotes
}
[download]

Which is going a bit further than the direct solution of

$string =~ tr/\s'/_/d;
[download]