About the usage of "make my day"

A paragraph goes like:

A cockroach was caught by a man. About to be put to death, it snapped to the executioner its last words, "Go ahead and kill me, you coward! You're just jealous, because I can have your wife spooked to scream while you can't."

In this scenario, is it okay if I use "make my day" instead of "kill me," as in Clint Eastwood's famous movie quote?

Thank you.

"Kill me" would mean to execute the cockroach, whereas "make my day" would mean to make the cockroach very happy.

As in -

Go ahead and make me happy, you coward! You're just jealous because I can have your wife spooked to scream while you can't."

Which doesn't make sense in your context. How can the cockroach be made to feel happy if he is about to be killed?

According to the Oxford Dictionary

make someone's day

Make an otherwise ordinary or dull day pleasingly memorable for someone.

So, no, that idiom doesn't mean "put me out of my misery" in any scenario. @Xanne has already explained the scene in Dirty Harry.

As pointed by @Justin, how can a day be memorable if you're dead?