What is the reason for not wanting to log these? It really shouldn't harm anything. If it is filling up your disk partition then something is terribly wrong, and I'd look into how you can deal with that.
If it's just because you don't want to see these requests in your reports, then the appropriate way to go about that is to configure your reporting software just to ignore those requests. Many log analysers would already have a feature to do this, or may already be configured to report them differently.
That way, you still have the data if you need it (it may come in useful, for example when seeing how many people are still using the old URL) in the future.