Silverlight's security model and sandbox do not allow "transparent" (user code and applications) to perform p/invokes, trusted operations, or anything of that sort.
If you already have an ActiveX control installed and available to the web page, you'll need to use the HTML Interoperability features of Silverlight to marshall the data yourself. There's an MSDN article about the HTML bridge that's specific to Silverlight 2, but you'll find it the same in newer releases of Silverlight as well.
This assumes that your ActiveX control is accessible through browsing scripting / JavaScript already.
Though some marshalling of numbers and some other primitives works well in the platform, you'll likely end up moving all your data from your ActiveX control through the use of strings, then parsing it back on the Silverlight client.
This might at least enable your scenario.