If you use a diffferent domain name, or a subdomain, and (assuming barebones) no php / no session_autostart, there should be no cookies. It's pretty much Best-Current-Practice of the major sites (and even small ones), and works well.
I'm assuming you're looking to speed up your site -- the first, and most effective way (short of using a CDN) would be to have a subdomain or separate domain for your images. It doubles the pipelining bucket (since pipelines are per-FQDN). A great help.
Last, turn OFF compression on your image server; unless it's serving out pdfs or bloaty raw-files, you take a CPU hit and gain no bandwidth speed over trying to compress an already-highly-optimized file.
Hope this helps!