I am a DIYer, so any pro responses could override my thoughts. 1/32" is nothing, IMHO. I installed engineered flooring several years ago over vinyl tiles glued onto concrete. The tiles were thin, but likely thicker than 1/32". Some of the tiles were loose, and I removed them. I did nothing to even the floor where the tiles were removed, because, as I recall, the installation instructions allowed me to ignore such minimal variations. The composition of engineered or hardwood flooring allow it to bridge over these. Also, because your unevenness is near walls, there will be minimal repetitive forces applied there. You could be double safe by applying a mortar-like product made to feather such variations. To me, this is easier and less messy than feathering by sanding.

You can get an engineered floor that is as good if not better than a solid product. We produce solid unfinished flooring but we also produce unfinished engineered flooring as well. Solid flooring typically has a 1/4" (6mm) of "sandable" or "usable" surface. Basically after you get 1/4" deep you'll hit the nail heads and so you can't sand below that point. Our engineered unfinished product has a 5mm wear layer. However, the engineered product is already pre-sanded to 80g which means once installed the amount of sanding that takes place is minimal. On a solid floor, most contractors will need to do a rough sanding to get the floor even, then one or two more cuts to get it smooth. Even if you have a very talented sander he is going to take 1/32 off in his sanding on the solid floor. That equates to roughly 3/100 which is nearly the difference between the 6mm and 5mm usable surfaces we began with. So in essence, you are getting very close to the same "usable" surface. Not to mention the engineered is more stable, will keep you from having to install a subfloor as it can be glued directly to concrete, eliminates transition issues between hardwood and tile or carpet AND should take less time to install. My two cents. Sam @ Real Wood Floors realwoodfloors.com

Our floor is white oak. Bruce Dundee Plank in butterrum. We've had it installed for ~ a year, no wear/finish issues. There is about 1500 sq ft installed in our house (bedrooms, hall, kitchen, dining, living and stairs), two mini doxies (whose nails aren't kept short) and we do wear shoes in the house.

Just keep going with the natural finish. Having slightly darker trim (in the same tones) should be fine. You have enough of the deeper coloured wood to allow the trim to stay darker...it is a way to tie things together. If you wish to change out the trim, you will need to look at changing out ALL the wood tones in the home...ouch! The trim+wood cabinets will allow each one to remain as-is without looking out of place. In design, the INSTANT you 'duplicate' something (colour, pattern, material, shape, etc) you create a 'design element'. Which is what will happen if you leave the darker trim alone. It will duplicate the darker colours of the wood cabinetry throughout the house = Tah Dah! Design Element! Congratulations.