Personally I wouldn't worry about wrinkled sheets.

The bottom sheet is usually fitted so I would be pulled more taught and the top sheet is covered by the blanket or comforter/duvet so you wont even see it.

If you want to naturally relax the fabric while drying follow some of these suggestions...

Dry Bed Sheets / Less Wrinkles

Don't be afraid of your sheets. They are sheets! You want them clean and fresh 😁 If white or off white I would wash in hot, minimum of detergent (never as much as is indicated on the packaging). I haven't bought Ikea sheets but they could very well wrinkle initially. They will become softer over time with repeated wear and laundering. By then you'll just be thinking about how lovely they feel at the end of a long day and you won't be interested in a wrinkle or two.

ALL of my sheets are either cotton or linen. No poly allowed. I use a blanket cover or if winter a comforter. No one but me knows if a wrinkle is present. I excluded DH because he wouldn't notice a wrinkled sheet or towel unless I were forcing him to wear it.

I don't iron either. He does his own. My childhood ironing days were not quite as traumatic as yours. My mother set up the ironing board in the living room and ironed while watching TV. If I took over for her I could see a soap opera which wasn't otherwise allowed.

Iron sheets? No way. Wrinkled sheets? Who cares -- no one is going to see them once the bed is made. Open the package, give them a good first washing, and enjoy!

I combat wrinkly sheets by putting them on the bed when they are ALMOST dry, handsmoothing out wrinkles. Then let dry completely before you finish making the bed.

They will get better over time.

I do a couple things I think help. I wash a sheet set as it's own load. I shake out and snap/fluff the sheets when I take them out of the washer before they get dried.

If the weather is good enough to use the line, I tend to hang my bedding out to dry more often than using the dryer. No wrinkles and smells great.

When the weather does not allow, I use a handful of the wool dryer balls in the dryer. Middling heat, not full on hot. Pull out and shake out and smooth sheets as soon as the dryer is done and stuff is till warm. I use the bed to smooth and fold on.

After that, I find that usually making the bed tidy with the blankets on top tends to take care of any wrinkles.

I don't tend to get new sheets much. I tend to find mine resale. But I do prewash cotton for sewing. Takes the sizing off the material and helps soften and account for shrinkage. Adding some baking soda to the first wash helps. Vinegar in the rinse helps too, but I don't recommend it since there is a lot of mixed information about using it in newer washers. I don't often find I need to do vinegar on material, I would imagine new sheets should have less sizing on them than a stiff cotton, lol.

Dry one sheet at a time in the dryer. Halfway through the dry cycle, pull out the sheet, shake it out, and put it back in to finish. Eventually, you may get used to slightly wrinkled sheets.

Ironing just the top hem takes about two minutes, it may be enough to feel "wrinkle free" and it's not like ironing a whole sheet at all.

Pull them out of the dryer as soon as they are dry, and make the bed or fold them. It’s no big deal if there are a couple little wrinkles.