I've used Tippex for years on crosswords and have won crossword comps with white out .
My reasoning is ,is that if it's clear to read they have to accept your entry .
Otherwise they would put a disclaimer .
here is a tip given to me by an A/Ber long ago...its fiddly but effective cut out a small strip if paper from the same page as the crossword, cut down to almost size of a clue square, paste it one side with glue stick [ you will be able to slide this small square until the glue sets] put over the offending letter or word then cut with scissors to fit, put in the correct letter.After one or two attempts you will become expert.
Or, even simpler, write with a pencil and only ink over the answers when you are sure they are all OK. I've tried using one of these erasable ball point pens as advertised in various mail order catalogues but they are not wonderful