With few execptions (bulk inserts in the bulk-logged recovery model), all database changes are written to the log first. Later, another process captures those changes that have been committed and writes them to the actual data files. The answer to your question is that you can't disable log writes.
If you have control over the upgrade scripts, then split the work into smaller batches and occasionally back up the transaction log between them to free up space. If the whole thing happens in a single transaction, then it must all be written to the log before any of it can be committed.
-Eddie