Yeah, you can upload the revised version to your project page (Root Access -> Edit Game -> Uploads), and it won’t require any intervention on my part at all.
If I delete the submission, will I be able to resubmit it even though the submission period is over?
If you’re just swapping the files (and keeping the project page), the project will stay part of the jam. So you won’t need to re-submit it to the jam.