I asked a similar question a while ago,one answer was to cut out a small square of newspaper from the same page as the crossword and put glue stick on the back and stick in place, its a bit "fiddly" to do, but you cant see it once done, then fill in the letter with a fine felt tip pen, works everytime for me and I have won too.
Nowadays I do the crossword in pencil then I go over when completed with a fine felt tip pen, then dry I rub out any visible pencil marks underneath.
good luck anyway you choose to do it.