I think that dedicated camera button may be hard to find... However, many Android devices have a way of quick launching camera. I think many Samsungs use a double tap of the hardware "home" button to launch camera under lock. Other OEMs have other means.
Check out GSMarena Phone Finder...
Phone Finder - search for a phone by feature - GSMArena.com
Put in your mandatory criteria and get a list of candidates, then shop those for price.
I went with 2015 and newer, I set the price to €400 or less as you may want to look at gently used.
Android.
FHD (1080p) or higher.
4.5" - 5.5" screen.
10MP or more.
OIS.
3000 mAh or higher.
In the free text I tried putting in Qi, but the filter didn't like it.
I got these 8 phones.
Phone Finder results - GSMArena.com
When you click into a model, you can add up to 2 more for side by side comparison.
OnePlus 2 has a good rep. So does the LG G Flex2 and I threw in the Xiaomi Mi5...
http://www.gsmarena.com/compare.php3...&idPhone3=6948
The later two have Fast Charge capability so that might be something to look at.