From your link you listed and according to its function, that HDMI-MiniDisplay adapter should work..
There are few points I want to point out:
Unless your external SSDs are Thunderbolt SSD - that USB-C devices can use "USB-A --> USB-C adapter" to achieve your need. TimeMachine can definitely uses USB-A/USB-C interface for its backup purpose.
That been said, I do use Thunderbolt 3 external SSD for extra storage (mainly for my music editing gigs) - I can see the significant difference between Thunderbolt vs USB-C.
Apple Cinema display also needs USB input for the speakers/Mic and webcam (a very outdated 720 grainy quality) plus three USB 2.0 ports. I do enjoy the speakers for casual purpose. If the additional functions from the Cinema display are important to you: there is OWC TB3 14 ports dock (It has the Mini Display Port; plus 1 TB port at back and 1 USB-C at front + 5 USB 3.1 Gen 1) might worth of taking a look.
Best