Try something like:

{
  local $db3->{RaiseError}=0;
  $sth_minus = $db3->prepare_cached("
       SELECT $column_list FROM $database_user_1.$table_names_r->[0]".
+'@'."$config{database_dblink_1}
       MINUS
       SELECT $column_list FROM $database_user_2.$table_names_r->[0]".
+'@'."$config{database_dblink_2}
  ");
  warn "prepare fails with $db3->errstr" if $db3->err;
}
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The errorcode is returned in $db3->err and the string in $db3->errstr not in $@.

Localising $db3->{RaiseError} is a way of locally setting the RaiseError attribute without having to rembember the state (probably not needed here, but it is a useful idiom :-).