Name spelling Jae or Jay

Our son’s middle name will be Jae. I want to spell it “Jae.” Both our names start with “J” and with my name being Jamie I like spelling it similar. - dropping the “mi.” My husband thinks Jae is more for a girl and wants to spell it “Jay.” So tell me, if you saw a boy with a middle name of Jae, Would you think anything of the spelling? Would you think that was the “girl” spelling. His name will be Hudson Jae or Hudson Jay if they help. What spelling do you prefer? Thanks!