You need to ask yourself a few questions, before you decide what path to take.
First of all, what is your cash flow per month and what are your fixed expenses without the debt? Secondly, what can you do to bring your fixed expenses down? If you bring your fixed costs down, will it leave you enough money to make payments AND put money in the bank? How did you get into the trouble? Was it from overspending or did unforeseen circumstances arise and you were unprepared for them? How secure is your job?
10k in debt should be manageable if you aren't already squeezed with high fixed costs. Even at 24% interest, the interest is only 200 dollars a month and the principal is a fraction of that. If you're behind that much on the cards, you must be having problems with cost of daily living.
If your cash flow isn't sufficient to cover your fixed costs and the debt service, then BK is probably the way to go. You'll only go further into debt and since your credit is already fucked, it will be harder to find someone to loan you the money to bail you out.
But I would evaluate very carefully my living expenses first. If you can cut costs by lifestyle changes, (smaller apt. or roommates, get rid of cable tv, eat at home, 7-11 coffee instead of Starbucks, coupon shop, cheaper clothing etc.) and cash flow enough to pay the creditors and put money in the bank for the rainy day, you should work it out with your creditors, because its the right thing to do.
The creditor who says that they won't work with you is full of shit. They don't want you to declare BK. If for some reason they decide to try and take you to court, then BK would be a method of defense.