Can I change iMac harddrive without taking off the display cables?

Sorry to say there is no means to replace your HD with a SSD without taking the display fully off. The problem is you need to fit your hands within the space and are more likely to yank and damage the cables and/or the connections which would be more expensive a repair!

So you you really feel like this is to much then maybe the best thing is to find a good Mac repair person near you and let them do it.

Frankly, I think you have better results adding the SSD Vs swapping the HDD out for it. You do realize your system has a spare SATA port which allows you to add the drive? While a bit more work I think its worth it!

Here's the IFIXIT guides for both directions:

• iMac Intel 21.5" EMC 2428 Hard Drive Replacement
• Installing iMac Intel 21.5" EMC 2428 Dual Drive Kit

Keep in mind your system depends on the HDD internal thermal sensor to manage its cooling if you replace it with another HDD or SSD you'll need to get this: OWC - In-line Digital Thermal Sensor for iMac 2011 Hard Drive Upgrade otherwise your systems cooling will not work properly.