Can I use jotform to create agreements and have people electronically sign them?

I don't want the agreement linked to my website. I want to be able to manipulate the agreement for each client, email it to them and have them electronically sign

You can add the agreement in your form through a Text field:

Or using the Short Scrollable Terms widget: https://widgets.jotform.com/widget/short_scrollable_terms 

Then, add the E-signature widget: https://widgets.jotform.com/widget/signature 

Let us know if you need more help, we will be glad to assist you.