I was wondering if anyone out there could give me some tips on breathing exercises that I can practice during my daily walk.
I guess that you're interested in a kind of breathing relevant to aikido (and any budo). If so, it is important how you breathe. I'd like to call it ki breathing.
It's belly breathing, more precisely with your center, and long extensions - especially of the exhalation, as mentioned by David above.
If you focus on exhalation and extension, it increases your power (as in budo, where almost every decisive movement is done when exhaling). If you focus on inhalation it leads to a strong sense of inspiration (as in the arts).
I have some ki breathing exercises on my website:
Check under the headline Breathing
Also check the Extension
exercises on the same webpage. There's one for walking.