I'm in the same boat, looking for waterproof, lightweight, non-sporty/city sneakers with a flat sole. I've searched for years and haven't found anything yet. For now I have tried:
- Regular sneakers. Absolutely not waterproof.
- Leather mid-top sneakers/chukka hybrids. The leather parts and stitching can be made reasonably waterproof using dubbin, unfortunately the tongue is fabric and will soak up water very quickly which will then leak inside the shoes, making the waterproofing useless. Wish I knew this before finding myself on my bike in a thunderstorm.
- "Waterproof sneakers" from Tropicfeel. Maybe waterproof, I can't wear them because they are way too narrow and extremely painful for my wide feet. Low cut means water can sneak in from the ankles down even with rain overpants.
Not sneakers:
- Good old Timbs. The most waterproof shoes I ever had. Still look like new after 4 rainy winters and regular care. Can't be worn for extended periods of time due to weight and drop.
Probable next steps: