Making IE .SWFs play as Shockwave files

Hi, again.
I solved most of the problem I had in the 'Flash 8.0 has stopped working' thread... but I have a new issue.

I have a number of .SWF files I exported from Flash 8.0 over the years, but on my new computer they don't have the Flash player icon - it's the IE icon. I can double-click and get them to open in IE, but I didn't have to put up with that on the old 'puter. Plus, I can't import any of these into Flash to use in my animating anymore. I just installed the new version of the Shockwave player, but it didn't adjust anything. How do I solve this problem?

In my previous post I eventually discovered that I needed to set Flash 8.0 compatibility to operate in WIn 95, but with these IE versions I don't know how to get there... if that's the problem. Thank you!