Every league inevitably has some owners who lead busier lives than others. This is no reason to leave them out in the cold when it comes to acquiring free agent players.
After your league’s draft is over, you should not allow free agent pickups until all owners have logged into your online commissioner software and all have submitted waiver claims on undrafted players.
Likewise, during the regular season, there should be a one- or two-day waiver wire claim period so all owners, regardless how busy they are, can try to add players to their teams. Once the waiver wire period is over, then you can go to a free-for-all free agency signing period leading up to that week’s games.