There are many ways but I don’t think there’s an expedient one as “without” in Korean. I would stick with -(하)지않고 since this works for all the examples above.
•눈 뜨지 않고 (=눈 안뜨고)
•번역하지 않고 (=번역 안하고)
•훔쳐보지 않고 (=몰래 안보고)
However you should not use it as “without” exactly. It doesn’t work this way; without your help (eg)
->너의 도움 하지 않고 =wrong
너의 도움 없이 = correct