Dont worry that you cant answer my letters quickly. I know that you are very bust working all day
long. So you should have apologized for being late with your answer to my letter
are these sentences correct and natural
Thanks

Question

Answer

Don't worry if you can not answer my letter immediately. I know that you are very busy working all day so you don't have to apologize for being late with your reply.

Answer

Dont worry if you cannot answer my letter immediately since i know that you are busy working all day long , and you need not / should not apologise if you reply late.

Yes , it sounds natural