1 day in Kitakyushu: both Mojiko + Kokura?

Planning to stay in Kitakyushu for 1 day in June. Will be leaving Hakata station in the morning and the hotel for the night is near Kokura station.

My question is if we want to do some shopping in Kokura area + visit Kokura castle, will we have time to do a quick visit in Mojiko + Ferry to Karato Fish Market in the morning?

So the itinerary could be something like:
1) Leave Fukuoka in the morning at 8am and go to Karato Fish Market around 10am for brunch + tour Mojiko area until 1-2pm.
2) 2-3pm: Come back to Kokura area and visit Kokura Castle+ shopping in Kokura.

Is this too rush or manageable? How much time should I allocate for Mojiko + Karato if we decide to go? Also is it easy to do this route without a car rental?

Thanks in advance!

It's rushed but doable. Really depends on what you wanna see and miss.

What shopping in Kokura is do be done that cannot be done elsewhere?

Thanks for your response. How much time do you think I need for Mojiko area? Will 1-2 hours be enough? Are there a lot to see or it's kind of open/harbor view...like Yokohama harbor?

Regarding shopping, we just want to check out some anime goods in Aru Aru. Never been there...so can't comment if I can do the same elsewhere?

Re/ Mojiko. Depends on what you wanna see?

Old port area (probs 50 different building and mini museums)
Old station building
Torroko train
Train museum
Walkway under strait
Viewing area for bridge and strait

For me its an all day affair.