That would be like car dealer asking "should I get a LOI before I let folks drive the new car." For a 7-day trial dont waste your time, or their's, on a LOI. LOI's are not worth the paper its written on.
A no commitment try-before-buy is almost always a great sales strategy for good software. Customers would have a hundred questions when they actually use your product. this is also a good opportunity to learn about how to sell to the next client by improving your sales pitch.
Not sure if your product is amenable to this, but one learning I would share is give a "shared account" for trial. for example the product could be branded in your name, other trialling companies could be using it at the same time etc.
say for example if you were sellling GMAIL, you would give them a 7-day free trial but they have to use an email and password you give them like username: test@gmail.com , password: test123 and other users will be logging in at the same time - trying sending and receving email, tagging mails, suggested replies etc.
I sell a product that allows customers to send messages via WhatsApp. I give them a shared account to play with as long as they like. but if they want a branded account , they have to pay upfront and only then i set it up.
back to the car analogy. Think of it like a demo car http://bit.ly/2ySHeTc . The client get a feel for the car but pays if they need one, all for themselves.