You're basically right; you just want to wrap the use part in an eval block. You don't have to use a string, and not using a string will be a little bit faster. Something like:

#!/usr/bin/perl -w

use strict;

eval "use DBI";

if ($@) {
  runwithout();
}
else {
  run();
}
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Update: Looks like you do need to use a string to get the effect you want. Above code has been updated. Also added use strict