This is not an ideal solution, but...

Since you're in a transaction, you don't have to worry about a race condition. As such, you can query for the matching records before you delete them.

my $suffix = 'FROM table WHERE blah blah';
my ($to_be_deleted) = $dbh->selectrow_array(
    "SELECT count(*) $suffix"
);
$dbh->do( "DELETE $suffix" );
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The first problem with this is performance. You'll be going to these same records twice. If it's a huge table, and the condition causes a full table scan, this is going to be really painful.

The second problem is that it's possible for $suffix to work fine for the "SELECT", but not for the "DELETE". That's not a huge problem, I think, because it will abort the transaction. That is, it'll fail instead of lie. I could be wrong, however. Not knowing what kind of SQL you have in $sth, I don't know if this is a potential issue.