The only "evidence" is Mon*Star's cameo in Thundercats (2011).
As you have already noted, a character closely resembling Mon*Star briefly appears on a screen in the episode "Legacy" of the 2011 Thundercats series. Depending on how strongly one interprets this, this could be solid evidence that both Thundercats and SilverHawks share the same fictional universe. The MTV Geek column on the MTV web site went in this direction with their interpretation:
This clip CONFIRMS the inclusion of both the SilverHawks and TigerSharks in the new ThunderCats universe! We can clearly see SilverHawks nemesis Mon*Star and TigerSharks hero Mako in the clip below.
Here is Mon*Star as he appeared in the original SilverHawks series:
Personally, I would back off from going as far as the MTV Geek assessment, for the following reasons:
the Thundercats remake has a significant nostalgia factor, as you have mentioned already in the question, and this could be an easter egg for out-of-universe effect only;
we do not have independent confirmation that the image on the screen in "Legacy"
is definitively Mon*Star, despite the resemblance;
it could be a new character with an appearance inspired by Mon*Star.
While there is no evidence to rule out that Thundercats and SilverHawks occupy the same universe, there are also no independently-verifiable statements that say that they do.
Of course, the two original series were made by the same studio and shared writers and many of the same voice actors. It is therefore natural that the two series would share some common themes, and the shows were always regarded as "siblings" in a sense. That's likely the best that we can say.