Meh, there's 4,600 seats, minus season tickets and opposing team fan single-game tickets already sold. Announce after the last home game of the year against Vegas and you're fine.
I think the dampening effect on ticket sales at Mullet would have to be weighed against the need for a possible SLC group to sell season tickets and build up enthusiasm for the team there. The fact that the Mullet is so small makes that consideration even smaller, so I'd agree it isn't terrible for the Arizona team to be left as a lame duck franchise, if this thing were announced before the season ended.
The only possible reason why it would be delayed is it would be super embarrassing if the Coyotes suddenly went on a tear, made the playoffs and then went on a deep playoff run. If they were to do that, the only narrative during the playoffs would be that this team that won't exist in four months was doing damage during the playoffs. It might make for interesting headlines but there are 15 other playoff teams that would lose out on profile, including, likely, the one that wins the Stanley Cup.
Announcing unsettling news is tricky business. You want to avoid it disrupting the key stories of your organization. In the case of the NHL, the next big stories are the outdoor games and then the trade deadline. Then there's six weeks before playoffs start, when you want the narratives focused on the games themselves. Arizona's last home game is April 17, which would be too late.
I'd say if there was a relocation announcement coming, and I wanted the ideal time to make it, I'd target around the 1st of April. The club will be on the road for a few games so there will be time for the immediate anger to subside (less likelihood of fans showing up and throwing stuff on the ice, for example), and that gives the SLC group a full six months before opening day to get all their ducks in a row, while using the current playoff season to build up the hype and sell season tickets.
Ultimately there's no good timing for this, but you work with what you got. And to fully disclaim, I am not advocating the team move, but just gaming this out a little bit.