The way you have it is the more natural way to say it (and indeed this expression is often said with exactly these words in English). The English simple present tense is used to describe an ongoing situation or a general truth, like this one. This is true even if the event that you are interpreting took place in the past. Example:
Cheryl: I broke my leg last year.
Alice: Well, what doesn't kill you makes you stronger.
Cheryl: Actually, it made me a lot weaker, because I could only walk on one leg.
You could make it past tense if you were describing a specific event, but that would be a little weird, since the present tense version of this specific proverb is a well-known phrase:
Cheryl: I broke my leg last year.
Alice: Since that didn't kill you, that must have made you stronger.
Cheryl: Our friendship is over.
Finally, you can use the past tense if the maxim is no longer relevant.
Alice: When I was young, what didn't kill me made me stronger.