Is it OK to use an 8 Ohm tubed amp to power 16 Ohm speakers?

It will be fine but technically it's better to match as close as possible. 

Air Tight is right, trust them. You could try the16 ohm tap on your amplifier and compare the sound to the 8 ohm. It’s possible you may prefer one over the other. That’s a sonic/sound character choice. However either speaker tap is certainly safe and acceptable to use.
Charles

There is no chance of physical harm to either the amp or the speaker to use any tap on a tube amplifier, so it is worthwhile experimenting to see which sounds the best.  One combination may sound good under one set of circumstances, but not another (e.g., one one combination might run out of gas earlier than another so it would not be as good when required to play loud, but, it may otherwise sound better).  

If you actually do have an unusually high impedance speaker, an amp with an unusual 16 ohm tap might offer a theoretical advantage.  I presume that 16 ohm tap means a smaller turn ratio in the output transformer which may mean better sound.  Again, it is a "may" because you might prefer the slightly better bass control and smoother frequency balance of using the 8 ohm tap instead (higher damping factor).  Again, when you have the time to make the internal switch, just try it.

Roger Modjeski of Music Reference recommends using the lowest tap that gives you enough power for your speakers (almost all tube amps put out less power as impedance descends). He calls this "light loading". You can use the 8, 4, or 2 ohm tap for 16 ohm speakers, and the 4 or 2 ohm tap for 8 ohm speakers, but not the opposite (taps higher than the speaker’s nominal impedance). The lower the tap, the higher the damping factor and the lower the distortion, generally speaking.

I'm aware of the "light loading" method and have tried it.  Like most things concerning High End audio variables and circumstances come into play. My speaker's are 14 ohm and my amplifier has 8 and 16 ohm taps. When using the 8 ohm tap the sound quality is very good.  When using the 16 ohm tap there is a noticeable improvement overall.  So both choices are quite good but the 16 ohm tap was clearly better. 

Again I believe that the results are going to vary depending on the individual components and listeners involved.  When ever possible listen to all available speaker taps and decide which one is preferable. 
Charles