Can I include in my email the edit link as a URL and not clickable link?

You will have to manually create the link if you want to display it as a URL instead of a clickable link. Please follow the steps below:

1. Type this URL in the email http://submit.jotform.com/form.php?formID=

2. Add your form's ID to the end of the URL http://submit.jotform.co/form.php?formID=62832344984969

3. Then add the following text to the url &sid=

4. From the Form Fields dropdown, insert the Submission ID at the end of the url

5. Finally, insert the text &mode=edit at the end.

The URL should look like the one below. The yellow highlighted text needs to be your form's ID 

http://submit.jotform.com/form.php?formID=62832344984969&sid={id}&mode=edit

If you need further assistance, please let us know.
Regards.

Something might be going wrong,

http://submit.jotform.com/form.php?formID=62335874056662&sid=351932716581478205&mode=edit

 This is what I have but it isn't working.

I tested your form edit URL link and it works, but it is important that you're logged in in order to be able to edit the submission:

Please log in and test.

Let us know if the issue persists so we can investigate further.

Thank you!