Considering that Jefferies (and others) were war veterans, there were no "Mark" designations for ships in the 1960's and the context in which the primary phaser schematic is presented (to tell the viewer what kind of phaser he is looking at, not what kind of ship), I'd say it's pretty clear that the "MK IX/01" designation refers to the primary (long range) phaser.
The first of about 100 Mark I
Swift Boats became operational with the U.S. Navy in August 1965. Fourty-six Mark II
Swift Boats went into service in late 1967. Thirty-three more Mark III
Swift Boats went into service from 1969 to 1972. Clearly, actual craft
had "Mk" designation with the U.S. Navy--not just armaments on
craft. With these new Mark I and Mark II Swift Boats being the newest and hottest things in use in Viet Nam, it wouldn't be too surprising if Matt Jefferies had selected a "futuristic" "Mk IX" for his "Constitution Class" display for "Space Seed."