Hi fellow Japan travelers

I am looking into a Japan trip in the spring of 2025 with my wife and our future 10-12 month old infant at that time. So far when my wife and i travel its always just us two. And now we will have our infant for this upcoming Japan trip. And i've heard how strict Asia and European countries can be with occupancy. Looking at Hyatt website, This hotel caught my eye since its a cat 4 hotel so i can use my 2 annual certs plus points to top it off for other days. Then when i try to price it with adding an infant. The free night cert option went away. The cash price for 2 was 52k yen, while adding an infant turns to 53k yen. that 1k yen is like 5 bucks USD so i'm wondering how others book this hyatt or any other hyatt or other hotels with infants? Can i get away with just booking this using the free night certs? Or would they just have me pay the additional for infant in cash?

Thanks