Am I right in thinking we can only register 25 players (not including any players under 21?)
Yes, but U21s don't count towards this total.
But the only U21s anywhere near first team reckoning are Woodman and Armstrong (hypothetically in the latter's case).
Merino and Aarons?
Good shout, Merino is technically "U21" but Aarons isn't. Makes that signing look even better.
Players born on or after January 1st 1996 for 2017/18 season.
http://www.nufc.com/2017-18html/squad.html
I counted 28, excluding the likes of Good who is nowhere near the 1st team. If this means Riviere and Saivet are left in no-man's land, so be it since they are 'invisible' men anyway.