You can get some benefit even without learning the order of the alphabet. If you divide things to groups by their first letter, even if the groups are sorted randomly, and the things in one group are sorted randomly, the search time should be at least 10 times shorter.

As a bonus, you can switch to this system gradually. Create empty groups for each first letter, and consider everything else as an "unsorted" group. When searching, first look in the group with given letter, then in the "unsorted" group. When finished, always put the thing into the group starting with that letter. Your system will sort gradually.