this is fiddly but looks better, you need a glue stick [ Tesco is the cheapest] cut out a strip of newspaper from the same page as the crossword mistake then the paper matches, then cut it down to the size of the offending square[ or two] glue the back and paste it, then place over the square and press down , then cut off the surplus, leave a few mins then put in the correct spelling, as I say its fiddly but when finished looks neat, practice makes perfect and I have won once with these corrections.
Alternative W.H.Smith sells a pack of three ball pens with eraser that you can erase for 24 hours after writing.