I had this exact same need. The way I solved it was to create my own interfaces that live in my class library and I use those to get access to the current HttpContext regardless of whether the library is running under a 4.5 http context or a MVC Core http context.
To explain further, both the ASP 4.5 framework and the ASP Core Framework have an HttpContext object with associated Request and Response objects but they are defined in different namespaces and neither framework knows about the other framework's namespace. So What I decided is that I needed my library code to have access to an IHttpContext that was defined in one of my namespaces. And that IHttpContext would use an IHttpRequest and IHttpResponse that were also defined in my library's namespace. And finally, that IHttpRequest uses ISession, IHeaders and ICookies that are defined in my namespace.
With these interfaces defined, in my ASP 4.5 website I can now at the web layer create an HttpContext class based on my IHttpContext and have that class basically wrap the ASP 4.5 HttpContext object. My HttpContext object could then be passed into my library for use.
And in my MVC Core website I can now at the web layer create an HttpContext class based on my IHttpContext and have that class basically wrap the MVC Core HttpContext object. My HttpContext object could then be passed into my library for use just like it was when I was running under the ASP 4.5 environment.
So in the end, my library doesn't know which HttpContext object (4.5 or Core) it is actually accessing under the hood because it just knows that the object is has access to confirms to the IHttpInterface defined in it's library.
One final note, to help navigate name conflicts, I actually named my interfaces this way:
IAppHttpContext
IAppHttpRequest
IAppHttpResponse
IAppHttpSession
IAppHttpRequestHeaders
IAppHttpRequestCookies
Note that not all the functionality that is available in HttpContext 4.5 is available in MVC Core. The two are very similar but there are a few differences. The biggest difference is that MVC Core Session can only store byte arrays or strings whereas 4.5 session can store objects. So my IAppSession only supports storing byte arrays and strings and I have to make sure all my library's session needs work with that (all the objects that I need to store in session need to be serializable).
As you can imagine, implementing this is a bit of work, but in the end you will have a library that can access HttpContext and not care if it's running under a 4.5 HttpContext or a MVC Core HttpContext. Kinda neat.
Good luck.