This is interesting, because my initial thought when I read your question was, "Isn't that rather open to Fraud?"

However, lets park that just for a second. 

So first of all, you will want to know the scope of this request. What documents/emails/requests etc, will this electronic signature be used for? Who will it be used for? Are there any people this doesn't apply to?

Secondly, I would imagine you will need some form of Audit trail to show them that an 'e-signature' has been used, and a report function which tells the person that it has happened? This can possibly configured so that it can be turned off, or maybe have a dashboard so they can investigate it themselves?

Thirdly, are their any levels (for example for financial transactions) where there is a threshold. So for example, lets say they were using the e-signature to request a payment, does that User have a 'credit limit' that they can authorise up to?

Fourthly, is there a override feature, for example when they want to use a real signature or add a note  to it? 

Some of these may depend on what the functionality is used for exactly. So to help you I would go into 'Path' mode. To do this, just either build yourself a Process diagram or think of each step - what are the possible outcomes and does your new functionality have the ability to handle that possible path? It doesn't matter how obscure it is (although don't drop down to "What happens if a meteorite hits the building") it might happen. If your stakeholders don't want to include it, then that's fine, but get them to put that in writing so you can cover your back. 

As a facilitator, start off with some simple questions about the general idea of the project, then gradually go into detail about certain points. The conversation should be fairly natural. If you think of something later, or you aren't sure about something then ask them again. Its also always a good idea to put all of your notes into an email and get them to confirm that's what they mean. Call it a very early draft of your Requirements Document ! 

If you have any particular questions then feel free to ask.