Is there any good cure in Midway for Japan's lack of search capabilities?
There are some differences in play between the original (60s) and updated (90s) editions of Midway - not least of which is where ships come into the game from (the newer edition uses hexes instead of a uniform grid, too). Based on this question mentioning the 7 squares rule, I'll assume (and answer as if) you're looking at the older edition.

There's not really a "need" to compensate for the Japanese player's fewer searches. Using a T1 or D1 (or F1) to search, I suppose, could be done, but you should be able to extend those out to 14 squares (the limit of a plane's range) - and allow a kamikaze attack by that plane (or squadron, if you sent more than one) if they happen to find anything .. might even consider upping their AF by 1, reducing their die roll by one, decreasing the DF by 1 of the ship, or a combination of the three. Of course, if they find nothing, you've lost those aircraft.

You might cut the number of American searches to 3 from 4, but that's not a big difference either.