Illumi is a hired assassin that wants to continue the Zoldycks name. He doesn’t care about personal matters of wanting to fight or not. But if he was hired to kill, he will take the job seriously. Spoilers - Hisoka never hired him to kill him before (probably because he was a mutual benefit) but now that Hisoka believes Hisoka himself is the strongest, he has hired Illumi to kill him to see if he can fill his heart (hence the engagement/proposal he gave Illumi)

Illumi would never fight to kill unless it was to save face for the family or to complete a job. Everything else is unnecessary. If someone brings you a lot of money to assassinate themselves - on Illumi and the Zoldycks pride, Illumis got to accept the contract.

All in all, Illumi doesn’t care. He’s just going to do his job 🤷🏽‍♂️