Can we start clan war league without our clan leader?
You can! From the wiki page on Clan Wars:
Leaders and co-leaders can take their clan to war by opening the clan war screen and pressing the “Start War” button.
As long as your clan has an active co-leader, you can still participate in clan wars.
I can enroll my clan into the Clan War League (which is completely separate from Clan Wars) as a Co-Leader during the opt-in period. I can also choose which clan members are in/out of the CWL, and change participants each war.