Even if you manage to install Snapchat, the first run will require Google Play Services that you can remove afterwards. If you don't have Google Play Services, install it and then install Snapchat and once everything is up and running you can remove the Google Play Services and use the application normally.
For this to happen, you just need to download the Snapchat APK file. The latest version of the Snapchat APK can be obtained through the APKMirror: http://www.apkmirror.com/apk/snapchat-inc/
