Solid Edge currently ignores your default browser preference and always calls Internet Explorer directly. Because of this there is no direct way to have Favourite Links open in your default browser or any browser other than Internet Explorer.
However, it is possible to point a Solid Edge Favourite Link to an HTML file local on your computer, which in turn would then launch Internet Explorer, force Internet Explorer to launch your preferred web browser, and then quietly close Internet Explorer so that you are left with your Favourite Link opened in your preferred browser.
Unfortunately you will always see a "flash" of Internet Explorer launching then closing. There is no way around this that I am aware of.
The files necessary to implement and installation instructions can be downloaded from my GitHub site.
This has always been one of those little annoyances that have bothered me over the years and I have attempted to resolve without much success. When I saw your question, I used it as an excuse to tackle this issue once again. This time I was more successful. Not exactly the most elegant as in not quiet but it is still a functioning solution if you really have to have one in place.