Hard Cases tips and recommendation (for flights)?

Hello! I just began playing bass and bought my first instrument a month ago; unfortunately, I will be moving to a different country! I have Yamaha BB234 bass and was looking into 1SKB-44PRO case; however, the sales expert checked that my bass won't fit into it, instead, recommended me SKB 1SKB-FB4 Shaped Standard Bass Case .

I am worried since that one does not have "ATA" or "flight case" mentioned anywhere so I was wondering if I should get Gator Flight Pro V3 instead?

I just wasn't too sure if the shape difference between the two is a huge difference, or if Gator one above is more reliable since it says "ATA". Sorry if this is a repeated questions; I researched a lot but couldn't come into conclusion!

Please let me know of other options too if anyone knows a better one or ones you tried before!

+ I unfortunately can't carry it or gate check due to airline policy; I will be going on 14 hours flight. Please let me know of other travel tips too please!