9.3.5 is the best version iOS 9 there is, so you should definitely install it.
So far.... There are no nag screens to install iOS 10. Thank goodness. I haven't installed it, and I don't get any nag screens to do so. I hope it stays that way.
Addressing both the points you made here:
I've just been suffering the nag screens for the last couple of days. So no; that issue hasn't gone away.
And the nag screens are worse!
Previously; it would simply wake you sometime after midnight, and you could work through the "remind me later" to get rid of it. Now; "remind me later" is code for "enter your passcode and I'll automatically install for you".
So no; I can definitively state that upgrading to 9.3.5 was a mistake, and I dread to think how badly the updater in the next version is going to operate.