yes there is a little board you can get that converts SATA to IDE. (what people call IDE is technically ATA, specifically, PATA)
and if you google for SATA to IDE adaptor you see a picture of a little board with a SATA connector and an IDE connector.
Any cable it comes with is not what does the conversion so is not a conversion cable.
They are very cheap, like $10.
As for your question about cables, there isn't really an issue. There's no special cable.
You need a SATA cable to plug your drive into one of these adaptors just as you would normally plug it into a motherboard. You can get one that has a SATA cable or one that has it separately.
Some of the little boards have a male IDE connector like a motherboard has, and like the back of a PATA hard drive has. And you need an IDE cable, these are Females both sides, and plug the thing in. Other adaptor boards have a female connector on the adaptor board and you plug the hard drive in directly.
Some of the little boards are one way. (IDE to SATA. Or, SATA to IDE). Some are bidirectional, and have places one can plug the SATA cable - one for SATA to IDE, one for IDE to SATA. You obviously want a SATA to IDE one. Or a bidirectional one. Though a bidirectional one isn't as cheap.
On Amazon, I see SATA cable for a dollar. A bidirectional adaptor for $7. A one way one for $0.40 In some cases, links saying people that bought this bought this. So why you're worrying about the cost I have no idea. I guess you didn't google for an adaptor and see the prices, and you weren't able to guess that an adaptor wouldn't be expensive.