I doubt WiFi from the camera will satisfy.
Best I know (often wrong) you can only transfer jpgs via WiFi.
USB OTG adapters on Amazon, also known as USB Host
http://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Daps&field-keywords=usb+otg
Most fairly modern androids have USB Host support.
You'll need a file manager app installed.
Samsung includes one that's a bit of a kludge but it does work.
Plug a USB Host mounted drive into a Samsung, the file manager pops itself open with no other operator action needed.
My new Motorola has no OEM file browser.
On Android versions, Kit Kat and newer, you cannot write to a device installed microSD card with anything other than factory installed apps.
You can sure write to the device's internal memory, you can also write to USB Host connected devices.
From Amazon again, a thumb drive sized USB SD Card reader;
http://www.amazon.com/Sabrent-SuperSpeed-Windows-Certain-Android/dp/B00OJ5WBUE/ref=sr_1_1?s=pc&ie=UTF8&qid=1463695508&sr=1-1-spons&keywords=usb+card+reader&psc=1
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Plug the thumb sized reader into the USB Host adapter, insert the camera's SD Card into the reader, plug this three piece assembly into the Android's USB port, copy/paste your image files including raws to the Android's internal storage.
You'll need to prepare adequate internal storage space in advance.
Like in Windows when, ideally, USB devices should be "Ejected" prior to removal, USB Host devices should be "Un-Mounted" prior to removal.
Once unmounted, insert a fresh SD Card, copy/paste back from internal storage to the USB Host mounted SD Card, that's your backup.
Check your backup, then clear the internal storage making ready for the next go round.
I like Ghost Commander File Manager on non-rooted Androids, not bad for rooted ones too.
https://play.google.com/store/apps/details?id=com.ghostsq.commander
There are several other good file browsers;
https://play.google.com/store/search?q=File%20Manager&c=apps
I've used Astro and ES, both got the job done.
Paid for versions I've not found worthwhile unless the device is rooted. If rooted, Root Explorer is amazing.
All this File Explorer stuff does the same thing as Windows Explorer, copy/paste, move, delete and such.
While touch screen file browsing & file management isn't quite as easy as mousing the job on a PC, the same tasks are readily accomplished.
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Again, Kit Kat or newer WITH a built in file browser, you CAN use the device's microSD card as a shuttle as you'll have full write permissions.
Kit Kat or newer WITHOUT a built in file browser, forget the microSD, use internal storage for shuttle and a 3rd party file manager.
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Once you escape the Canon camera's 'environment', you are no longer working with images as such, the images are now just files.