philippulus
Static Build.
Usually, but not always, static builds are distributed as *.tar.gz downloads.
You're out of luck on TorGuard VPN and Shutter. There's nothing currently available that would work under Solus unless you can recompile the Debian versions for Solus. At least one of the Solus devs have mentioned doing this for some of the packages available in the Solus repos, so it is doable, but I don't know how easy or difficult it would be.
However, there are other screenshot apps available in the Solus repos. Search the Solus Software Center app using the search term screenshot.
VPN alternatives...use the Tor browser or a proxy service like kproxy; both are free. Additionally, the Tor browser comes in a self-updating static bulid for Linux so you'll get some exposure to a static build.
VPNs aren't as private as they're advertised to be.
Stop Using VPNs for Privacy
Or, consider rolling your own VPN.
How to Make Your Own VPN (and Why You Would Want to)