Release brakes Giant OCR4 2006
There are two ways:
1. Deflate the tyre, put the wheel in, re-inflate. I had to do like this in the old days.
2. There are tension release devices you can put in the cable-housing. Shimano amongst others sells those for their direct-mount rear Dura-ace brakes that don't come with release levers. (item SM-CB90)
The alternative would be new brakes indeed.