Foreach doesn't require an actual array to work from; it's perfectly content to work on the list returned from split:

foreach my $entry ( split( /;/, $file_data ) ) {
  do { s/^\s+//; s/\s+$//; } for $entry;
  push @email_list, $entry;
}
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Of course you can use map and get everything in one statement.

print join( "\n", sort map { (my $t=$_)=~s/^\s+//;$t=~s/\s+$//;$t } sp
+lit( /;/, $file_data ) ), "\n";
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Update: Of course if you need the list later you can certainly store the return from the sort into a variable and print that instead.

my @email_list = sort map ... split( /;/, $file_data );
print join( "\n", @email_list ), "\n";
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