They would all follow Katakuri, Pero could try to stand up for his chance but nobody will really follow him instead of Katakuri, Kata is both better in power and character as well (if Pero is still alive and somewhat come back).
The only possible rival, but that is a distant second, for be would be Streusen as the cook of the BM pirates and basically an hidden YC, maybe even YC1 on oar or above Kata. But despite that imo he will keep being a grey eminence behind the curtain, even if Kata would most likely be harder to influence than BM in a way (BM was a mad psycho with tantrums which was both manipulable in a way but also ruthless when she get mad). Also since Streusen is most likely a "normal" character without any mental problem (well, the interaction between him and young BM could be a gargantuan problem but I don't think it would make a difference here) he could also left Kata be the new yonko as probably he is also his son, so he could even help him if that is needed at all.