As far as I understand, you can use any DI in both Core and Hangfire. If you configure your DI framework through the regular Core stuff, you should be able to create an activator for Hangfire without any problems.
I haven’t executed .NET Framework 4.5 code from my Core project, but I’ve added NuGet packages that target 4.6 without any issues. If you don’t use methods that aren’t available in Core, everything should work fine!