Cash can't be traced, but credit card transactions can. If the deal goes south, you'll never get your cash back, but you can dispute a credit charge. If you have enough cash to buy the diamond, leave it in the bank where it's safe and pay your credit card bill in full when it arrives. If a store requires cash or check only, it's time to leave. Don't be lured by bargains for cash, you'll soon find it was no bargain.
Any legitimate jeweler takes credit cards.
Apply only if you have good credit. If your credit is ok, but not perfect, try the useful Lending Tree Credit Card Search. Their free service gives you up to 4 credit cards willing to issue credit to you. Then try this Credit Card Finder For People With Bad Credit. Don't keep applying to credit cards, get rejected, and your credit history ruined further, find out who will approve you before you apply.