You are kidding about Intel Atom aren't you?
I have tried using Intel's 'low power' chips occasionally (by low power Intel mean low performance not electricity consumption). Every single time I got burned. Intel prefers to have their FABs crank out top end high margin products. They see every cheap CPU (cheap compared to other Intel CPUs) they make is a lost sale of a more expensive CPU. They put bugger all effort into the small side and it shows up as hardware that promptly becomes non-functional and unsupported.
If you are stuck with a few ancient x86 binaries try them on ARM with QEMU. It is often sufficient and has an excellent service life. If that doesn't get the job done, go for a normal mass market Intel or AMD device. Economies of scale get the price of a complete system close to Intel's low power efforts and the service life will be two or three times greater.