That two-beat style under the head is based on a 2/4 march. You can hear the piano playing stride style (ooom-chuk-ooom-chuk) and you should take your cue from that. They didn't always use ride cymbals back then and the time was largely kept on the snare and bass drum. Though, in that example he does go to a cymbal to change the texture. You can also use slightly sloshy hats (very lightly) to get some sustain. But don't lose the backbeat on 2 and 4. He's just playing quarters on the ride for the most part, not too many skip notes.