Flip a coin . . .
Both time frames are perfect time's to visit the Canadian Rockies . . .
Weather and crowds will be similar during both time frames. Fires are generally a non-issue during both those time frames as well (more common in late July-early August if at all) unless it's particularly dry.
Your critter statement confuses though. Are you worried about having an altercation with an animal ?? Or more so that you would rather see the wildlife while their young are still small ?
"Seeing" wildlife is one of the huge attractions to visiting the Canadian Rockies. You will absolutely see Elk (probably every day) and deer, and likely a few black bears. If you are lucky you might see a Moose. If you leave them alone (i.e.. keep your distance and respect their space) they will leave you alone.
Fall is absolutely my favourite time of the year in the Rockies but late Aug/early July isn't really considered the fall . . .
Flip a coin. If you choose either of your two possible time frames you can't go wrong . . .
