Laver's exact hard court record is difficult to give. In the pre open era, the sources don't divide exactly between hard courts and clay courts, in fact the British compendia always refer to hard court, when they mean clay courts. The British Hard Court Champs at Bournemouth were one of the most prestigious clay events in the early open era. Overall in Europe hard courts, ashes or sand courts were the names for clay courts.
Since 1968 we have a clearer picture, the pros mainly played on hard courts and indoor Supreme court, they played very few grass events in Britain or Australia (and Forest Hills) and some clay events in Europe and a few clay events in Florida, at Houston and Louisville and at the Canadian Open. Between 1973 and 1977 many US events turned to har tru, later back to hard court.
Laver indeed won a ton of important hard courts events in the open era, many Super Nine Equivalents, which are not all registered by the ATP or ITF. For instance, he won the SA open 1969 and 70, the Boston US pro 1969 (then on Hard court), the LA South Pacific 1968 and 70, the Berkeley event 1971, the Fort Worth event 1967-1971, the Delray and Honkong events in 1973, the Palm Desert and the rich Alan King Las Vegas events 1974, most of them frequently. Many events of the WCT tours were indoors or on hard court. Even in 1975, Laver set a WCT record, winning 4 tournaments in 4 weeks (i think all on hard courts).