Option 1 results in a very twisty exhaust path while option 2 is obviously a ton of work.
Venting microwave through wall stud in way.
Studs run vertically through a wall.
I saw this done on this old house when they installed a new microwave hood on an outside wall.
Think of an turning into a line with a box in the middle.
Buy the sheet metal boot that converts from 3x10 rectangle on the top of the otr microwave to 5 or 6 inch round duct.
Seal all joints with metal tape and get a quality exterior hood with an exhaust flapper.
If you don t want to cut the stud install 2 rectangular ducts on each side of the stud and split the original duct into two.
Attach two flex elbows and steer around the duct and straight out the wall.
You will have to remove quite a bit of drywall and most likely that wall cabinet directly above the oven.
The manual for the microwave says to absolutely not use flexible ducting.
It appears when this house was built provision was made for venting out the rear of the microwave into the standard 2 4 wall up the cavity inside the wall then up through duct work in the attic through the roof.
Re install trim or siding.
My microwave oven is mounted to an exterior wall above the stove.
Sacrifice the cabinet above the stove by snaking an exhaust duct up from the hood over to one side of the stud and then through the wall.
Your proposed opening for the exhaust is pretty close to the underside of that cabinet and the header must go above the exhaust vent.
Just use flexible dryer vent and be done.
Get a dryer vent going from outside to inside of the house.
Basically tear down the wall to install a header saddle jack studs etc.
If the two rectangular ducts have a combined area greater than that circular one you wont have issues with flow restriction.
Line up microwave to duct and connect by placing it on the wall bracket or connecting bolts above.
First double check that your floor joists are lined up well enough that you can get a 10 duct through the floor where you need it.
Use 3m flashing tape or vycor or tyvek tape to assist ensure that water will not enter the building envelope.
It is designed to work like a hood.
Can anyone think of any other options.
Photo of unit installed it was heavy and bulky.
Connect it all with a piece of flexible dryer vent hose.
Basically i would start by breaking out the drywall around the proposed opening and that stud in the middle.
From microwave up into the cabinet is what you have now.
Total distance is about a foot performance will be barely compromised.
A stud in a wall supporting or otherwise can be cut and boxed.
I d cut a generous square at the bottom of the wall so you can cut out the plate in the stud bay.
This usually takes two people.
But the builder just left the microwave s fan blowing back into the kitchen.
