but I cannot risk having no job at all.
As a contractor, you need an emergency fund that can fully sustain you for 6 months to one year.
If you don't have such a fund, it either means that you're not asking for enough money or that you're living above your means. Or maybe it could mean something completely different.
But whatever the reason is, you need to work on rectifying that situation. Either cut your expenses, or ask for more money, or better still, work on both those levers until you can get that emergency fund built up.
I would always ask for it around this mark
From now on, come up with your own contract. Set your own terms. Don't let others set those terms for you. By relying on your own clients for your contract, you're leaving too much to chance.
I have another offer but I would need to accept it within a week.
No one can make this decision for you. You're in a bit of a pickle right now. But if you want things to start changing, you could use that second offer as an opportunity to ask for more money and set your own terms and see if that second party would be willing to accept that.
And if that second potential client refuses, then try falling back to your first client, but let your first client draft the contract (which is probably what you were planning to do anyway).
Also, you need to email/tell your first company that another company wants to hire you, and that without a signed contract, you're unable to make a commitment to them. And of course, don't tell them who that second party is, that's none of their business. And if they ask you what that second company is offering you, don't tell them that either. Tell them that you're not looking to start a bidding war, but that you're willing to go with whoever gives you a reasonable contract first.
And when your current client/manager calls you, you need to be a broken record about what you want from them.
(don't mind the title of that book, just read its customer reviews if you want to get a true sense of how freaking awesome that book really is)
In the meantime, continue to apply and interview for other jobs/contracts elsewhere. This is your contingency plan in case both offers fall through.