I can't see your Google picture(s) without logging in...
I believe these are the cups in question:
https://tos.trekcore.com/hd/albums/1x22hd/spaceseedhd460.jpg
I always thought of that color as a shade of gray rather than blue.
Among other episodes, this type of cup is also seen in The Trouble With Tribbles:
https://tos.trekcore.com/hd/albums/2x15hd/thetroublewithtribbleshd1126.jpg
I immediately thought of Where No Man Has Gone , which gives us a good unobstructed view:
https://tos.trekcore.com/hd/albums/1x03hd/wherenomanhasgonebeforehd395.jpg
That one is also gray, possibly with a bit more sheen, but also with a United Earth logo, or whatever it's called.
To my eye, the thickness, the white interior, and the width and shape of the lip thing at the top, look like typical disposable polystyrene foam cups, like these:
https://www.dartcontainer.com/about-us/dart-history/#event-1960
We typically refer to the stuff by the trade name Styrofoam, even when it's actually from another manufacturer. Anyway, these cups were still relatively new in the 1960s, as they had just come into widespread use at the beginning of the decade.
Those cups were plain white, so that means the ones that appeared on TOS had the exteriors painted to better fit into the setting of the show. Spray enamel paint is corrosive to that kind of foam because of the solvents mixed in, so it would have been an acrylic or latex paint brushed or rolled on.
I'm sure someone else out there has more specifics on these cups. Any clarifications or corrections are welcome.
Kor