I'm always a little reluctant to goo with a dedicated product as a lifehack, but in this case, my normal concern there doesn't seem to apply.*
You really, really should try Downy Wrinkle Releaser.
I've had your exact situation forever, and for any shity that doesn't actually need to have visible pressed creases, it's roughly as effective and much faster than most other methods.
You literally just spray it on wrinkled clothes, (or a creased area,) flatten the damp part with your hands, and the wrinkles come out.
So it's much faster than:
- Heating up and possibly filling an iron, etc.
- Dampening clothes and using the dryer (which is still better if you have a bunch of slightly wrinkled items).
- Steaming (machine or shower)
And you can travel with it for hotel use, etc.
- It has a pretty strong floral smell. I don't mind it, and it gets milder after a bit, but the initial scent is hard to miss.
- I wouldn't use it on anything really delicate, like silk, but most other possible solutions have issues there too.
- It's not quite as effective on wool as it is on cotton, but I still find it better for sweaters than ironing most of the time
*_ Normally, when there's a dedicated product for a task, it's not a great lifehacks answer, but that's usually a function of it being the one everyone knows, but is either not not available to the OP, or not appropriate for some specific reason. That doesn't appear to be the case here, and no one has mentioned it, and I've found it MUCH easier than the traditional methods for the case described.