The illuminated percentage is constantly changing, but the Nautical Almanac gives you that figure too. Although it only breaks it down to the nearest day. The percent the moon is illuminated on May 5, 6, and 7 is 99, 100, and 97, respectively. On those three days, the Almanac gives the semidiameter of the disc as 16.7 minutes of arc. No doubt it varies, but by too small an amount to be of any use for anyone to know it.

Needless to say, this type of information is becoming less and less useful to modern mariners with their electronic navigation.
I am concerned that it is only a matter of time before the Naval Observatory stops publication of the Almanac, leaving us old salts stranded on the shores of redundancy.

Its like shutting down the lighthouses...

If you're really anal about it, it is possible to calculate the exact second of full moon because the Almanac gives you both the Greewich Hour Angle of the moon AND sun for every even hour, and a method to interpolate it to the second. GHA is the angular distance of a celestial body from the Greenwich meridian. At full moon difference in GHA equals exactly 180 degrees, by definition.