Abandon all hope, ye who enter here...
Microsoft ceased all new development on Silverlight in 2013, and is only providing security patches. The Silverlight-on-Linux project (Moonlight) has effectively been abandonware since 2012, and only supported Silverlight versions 1 and 2 even when it was being actively developed (the last official Microsoft Silverlight release was version 5).
This sounds like a really, really deep rabbit hole to me. As in, unless this app didn't use any features beyond Silverlight 2 (and maybe even then), it would not surprise me if you need a full-time experienced Linux developer or three (to hack on the Moonlight code) to get this working decently on a modern distro and browser.
Nostalgia isn't what it used to be.