A nation's first carrier is pretty much always pretty ineffective. You need to make a ton of mistakes and develop a doctrine before they can be very useful, usually in the form of providing learnings for your 2nd and 3rd generation carriers. The KM is probably better off focusing on getting its own navally focused airforce with an idea towards maybe having carriers in the 50s or 60s but having aircraft trained for strikes against shipping now. Maybe do a little effort on escort carriers or very light carriers if you can get the British to buy off on the idea as mostly a form of disinformation.
I agree the KM would theoretically better suited by devoted to more long range maritime patrol aircraft/bombers. Something like a FW-200 but better. Something to scout out for U boats and occasionally attack unguarded merchant ships especially in the early war.