You can change the units if you want, but it's still a physical constant, and it could be stated in purely physical terms. For example, according to Wikipedia,

You can change the units if you want, but it's still a physical constant, and it could be stated in purely physical terms. For example, according to Wikipedia, the second is defined thus: "Since 1967, the second has been defined as exactly "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K)." Therefore, the meter may be defined as "the distance light travels in a vacuum in one of those cesium-133-related periods, times 9,192,631,770, divided by 299,792,458".