Hold the World Cup every 4 years, dont make any non-national teams, dont add any age restrictions to teams, allow players from all leagues to participate. The 2020 IIHF world championships IS the qualifier for the 2020 World Cup, top 8 teams in the spring tournament qualify for the one in the fall. The NHL does not have to re-create the wheel as the IIHF does all this already for them.
The NHL is still gonna want to make the 2020 World Cup as big of a cash grab as possible (At this point, as long as its best-on-best, I can live with that). Sticking adds over every square inch of the uniforms, ice, boards, cgi ads over the fans in the backgrounds, whatever. The World Cup will be held in North America each time, in September, on NHL sized ice, by NHL rules, and will probably be marketed towards North Americans only. Despite that, they will insist it is a 100% international hockey tournament. The tournament will probably be called the Bridgestone World Cup of Hockey presented by Mountain Dew or something like that because they can make a dollar or two more.
This tournament will make the NHL and the PA a ton of money whether or not the hockey is that great, just as long as some of it will be used to pay for the travel/insurance cost for the following Olympics. (Probably from the PA's half, and in return the NHL shuts down for 2 weeks every 4 years to give the players the time off). This way, the NHL gets their own international tournament they can milk the ever-loving crap out of, the players get to go to the Olympics again, the IIHF and the fans are happy because Best-on-best Olympic hockey is back, the IOC dont care either way what happens, Everybody wins...