When my DS started K his handwriting was no good at all. He could write letters but his own way, you know writing line the opposite direction. I never bothered to correct that, silly me. Also he had no idea how to write on the lines, his letters were all over the place. Pretty soon I heard that he needed lots of work on his fine motor skills. It took me a while to explain them that he was 5 after all and it didn't matter how much he could read or count, he had hands of a 5 year old.
That said his handwriting has improved dramatically in last few months. He writes slowly but he writes pretty good letters, even his teachers say so now. A year ago he would type on the computer most of the time, now he mostly writes.
I think your son will be ok. Let him write shopping list for you, list of things to do, thank you cards, letters to grandma ... He goes to Montessori, right? Ask them if they could give him more handwriting practice. You have plenty of time till September.