Karate-do ni sente nashi, "karate-do has no first attack" one of the 20 precepts of Master Funakoshi.
this is the appropriate translation.
if a person attacks you first it does not have to be physical, he can intend harm on you, if you feel threatened enough and your life is in danger
you can anticipate and do a preempted strike "sen sen no sen"

where as in your saying "A Karateka never strikes first" you would eliminated the kumite tactic of sen sen no sen.

there are several kumite tactics, the precepts take into account, a few are
sen no sen
sen sen no sen
go no sen
tai no sen

the main point is we do not attack first, but try to avoid violence, or defuse the situation by all other means, when all else fails and they leave us with little chose then we defend ourselves.

in a defensive situation you can strike first. a first attack my not be a physical one it can be a threading movement. if a person is going for a weapon, i not going to wait for him to use it on me. to this is the first attack his intent to use a weapon. i would be well justified in striking first.

This is not a literal meaning. What it means is that the karataka shouldn't instigate a fight or start a fight. That doesn't mean he or she can't throw the first strike. If you feel you are in danger and are fairly certain that your assailant is going to inflict harm on you then by all means take care of the situation immediatly and enough to the point where you can get away.

They way this has been phrased suggests that Karateka should allow their attacker to strike first, which is incorrect.

Would a more correct way be to say "A Karateka never strikes first"? (Which, contrary to popular misconception, does not mean the same thing.)