What would be the best way to purge/clean all null values in a Guava cache?

Question

I'm currently working with a Guava cache generated by Guava's cache builder and it has methods to remove all values, remove a set of values by key, and to remove a value by key. No, I cannot just not store the null values because they need to be stored for around 5 minutes.

Is there a better way to remove all null values after N minutes besides completely reimplementing a new cache where I can setup expireAfterWriteNanos when setting a value, or something like:

schedule at fixed rate(
   () -> {
      iterate through all keys to save which ones have null values
      cache.invalidate(iterable of all of those keys)
   },
   5 minutes
);

I prefer not to use this method because it's expensive to iterate through all of the keys