As you said, ApproveMe is a premium WordPress plugin that is little more expensive than your average WordPress plugin but it’s well worth it. It’s priced similar to Gravity Forms however it’s main focus is on generating court recognized UETA/ESIGN compliant release forms, contracts and agreements.
When it comes to signing legally binding documents that could end up in court the last thing you want (for you or your client) is a document that’s not court recognized. Especially if it ends up in the hands of a Judge. If I were in your shoes I would ask the client for the extra money and have them go with one of the UETA/ESIGN compliant options. Especially since it’s their business that could be compromised.
Here’s a few helpful links about security and the document signing regulations.
7 Ways to Protect Your Company from Contracts That Aren’t Binding
Security & UETA Compliance
ApproveMe Plugin Security