I think 'one' would be better than 'their' as one is undoubtedly singular, where 'their' hints at being plural. The entire sentence could be rewritten to use '

I think 'one' would be better than 'their' as one is undoubtedly singular, where 'their' hints at being plural. The entire sentence could be rewritten to use 'their', but I think simply swapping our 'his' with 'their' could change what is being said.