Silverlight has been out of support for years. IE just end of lifed this week. Neither are usable anymore. You didn't clarify exactly what you're using BHO or Silverlight for so it is hard to provide a replacement but pretty much everything you need is built into HTML5. You'll have to migrate your app and code. Alternatively if you need something more interactive then take a look at Blazor.
There is no migration path or workaround for these legacy technologies. You're going to have to rewrite your code.