Yes, this can be done. You must assume your application will only be deployed on Windows XP (or Windows Server 2003) or later, and then you can use what is called ‘registration free COM’ to make this happen.
Essentially what you do is create a manifest file for the ActiveX control DLL so the Windows loader & COM DLL’s know what its registration is without having to put that in the registry.
A walkthrough of what to do is in this article on MSDN:
Registration-Free Activation of COM Components: A Walkthrough
“Step 6” and “Step 7” in that article contain everything you will need.
I just tried this out on one of my own C# programs that uses a Microsoft ActiveX grid control (the old “MS Flex Grid”) and it works just fine. Make sure you create a manifest file for both your application and the COM DLL, and substitute the appropriate GUIDs in the right places. You may need to use OLEVIEW to dig out the right IDs to use from the ActiveX DLL if you don’t have them handy.