This is the point where you have to decide who you are as a businessperson - because what they're really balking at is having to sign a legally binding contract. And yes, there are plenty of folks willing to work without one. Hell, there are plenty of people willing to work at a tenth of your price. Doesn't mean you should be slicing your prices to make deals happen. Neither should you be this accommodating about a signed contract.
The question is, do you want to stay in business long term or not? I ask, because if you can't insist on protecting your interests during contract negotiation, it's only a matter of time before something big and ugly hits you. Believe it.
In my years working freelance, I've only had a prospect/client be unwilling to "go through that process" a few times. In every case, I held them to it, and they ultimately signed.. and then they tried to screw me (as no doubt they'd successfully done to others who fell for the "too much hassle" line). Those signed contracts got me paid and prevented court appearances in each case. One of those clients was a woman who was used to working with "gentlemen's agreements" (i.e., verbal only) until I forced her to paper; she found herself at ground zero of a serious IP legal action as a result of her lax attitude. As for me, I was free and clear - because my contract said so. Had that not been the case, I might not be in business today.. just as she isn't.
I've never once had a screw attempt or a legal threat happen from a client who didn't first try to get around signing a contract. The ones who sign are great to work with. The ones who actually negotiate terms honestly and respectfully are the best. Simply the best. Good contracts make good clients.
Contract negotiation is a normal part of business, and if you're willing to work without one, you're not in business: you're doing favors for promises. You're a hobbyist, and you're setting yourself up. My advice is to raise your rates immediately, tell them that a signed contract is mandatory, make the process as streamlined as you can (while still protecting yourself), and then work on your marketing. You need better clients.
And as far as clickthrough contracts go, no, they're not. Far too hard to verify the basic standards of contract law (i.e., meeting of the minds).