How can I view SWF files without Flash Player?
If you're looking for loopholes, because you know Flash Player is going away, you probably won't find any. Expect your SWF files to be useless by the end of the year.
There are some open-source alternatives to Flash Player (the actual SWF spec is open-source, so anyone can theoretically build a replacement), but in practice, it's really hard and there are a number of projects that play simple content just fine, but as the content gets more complex, start to diverge wildly from what you'd get when running Adobe Flash Player.
That said, Flash Player is going away at the same time that all the browsers are removing support for plug-ins, so if your open-source/alternative player is dependent on a browser supporting plug-ins, that's not really going to work.
The best answer is to go ask the content provider to convert their content to a supported technology that will work moving forward.