I would think WS relationship with Delta will most likely end, unless Delta add a lots more value to WS. This would be because of Onex close ties to American Airlines. Also, I can now see WS joining One World or Skyteam depending who WS ties up with in the States.
Onex has no signficant ties with AMR except historical and as a business I don't believe those connections carry any current weight.
While a takeover by Onex could be seen in negative terms there is also the fact that Private ownership gets away from the 1/4 by 1/4 focus and allows for potentially better long-term investment in re-making WestJet. Whether that effort stays on the current path or radically changes direction is the main question and all the thoughts here are so far entirely speculative. Onex has held some investments for many years and some for short periods - given the varied history, it is impossible to know what Onex's intents may be in this case.