Use Tasker to swipe lock the screen for 10 mins then require password thereafter
You are correct: an app called Tasker can do this. The feature you want to turn off/delay is called Keyguard: turning this off disables the password/PIN lock screen. So you could setup a task turning that off on the condition the screen is turned off, then wait 10 min, and re-activate it again.

Additionally, you might want to take a look at the Secure Settings addon for Tasker, which gives you some more fine-grained options towards this (and plenty of other benefits). Using this addon, you could e.g. have your device require the PIN/password unlock only once, and then not asking for it anymore (useful e.g. at home).