Having internet connected in any way at all can be considered a risk once extended support for Windows 7 ends on January 14th, 2020, even if it's for MC only. I mean, it'd probably be fine to do that, but to me it's purely unnecessary risk.
Personally? I wouldn't do it. If I still had a box running Windows 7, I'd either take advantage of the free Windows 10 upgrade that's still available (but not advertised) or switch to a different operating system, e.g. Ubuntu or Linux Mint. Sooner or later, JRiver (like all other software companies) will have to drop support for Windows 7 (like what's happened with XP and Vista). I'd say realistically that's probably 5 to 10 years away, depending on how much it's still used then.
Say what you want about Windows 10 about its flaws (and it has plenty) but there's no denying it's a more secure operating system versus Windows 7 or Windows 8.1.