Shinken roughly translates to mean "real or true sword", and as such, any traditional made and gunto Japanese swords could be called shinken. It's also used, as was indicated in prior responses to refer to a more modern sword used for iai and more specifically cutting use.
At your stated budget of around $8,000 you could actually purchase an older (koto to shin-shinto) real Japanese sword of good quality that will appreciate in value.
I just returned from Japan where I bought a shin-shinto that I am keeping in Japan for use in iai and iai-giri (cutting) so that I do not have to borrow one of my sensei's swords for testing and cutting practice (it is a paperwork hassle to bring swords in and out of Japan, more so in). This is a very nice piece with mei, the length is just under 29", and was in the $5500 range.
One of our Tokyo dojo members collects, polishes, and sells swords, and I have purchased several, including the last one from him. If you are interested in obtaining a sword, I can send you additional information on what is available and can get digital pictures for you. Export papers can also be arranged. I'm not sure where you are located, but usually my friend visits the U.S. several times a year to attend some of the sword shows here and brings several pieces with him. Obviously, a purchase like this is something you need to spend serious time on. I am returning to Tokyo in June and would be glad to collect any information and forward it to you if you're interested.