FIDE published the list of qualifying players in World Cup 2017 - Player's Contract and Qualifiers (July 2017), which makes a good starting point. I loaded the list into a database and produced the following chart.
The left side of the chart lists ten basic qualifying paths (a-j) into the World Cup, along with a count of players who qualified via each path. The right side of the chart lists further qualification info and a count of the players who qualified via direct competition (paths d-h). The qualifying paths are described in the FIDE document, Regulations for the World Chess Cup 2017 (fide.com; 'Handbook :: Regulations for Specific Competitions'):-
3. World Cup 2017
3.1. Qualifiers - There are 128 qualifiers (in order of priority): World Champion + four (4) semi-finalists from the World Cup 2015, Women's World Champion, World Junior U-20 Champions 2015 & 2016, eighteen (18) rated players as described in 3.1.2, ninety (92) players from Continental Championships, the one (1) highest-placed participant of the ACP Tour who has not qualified with the previous criteria, two (2) FIDE President nominees, four (4) organiser nominees , three (3) qualifiers from FIDE-approved internet events. If there are no internet events, the spot(s) will be decided by the FIDE President after consulting the WCOC.
3.1.1. Replacements - World Champion, semi-finalists of the World Cup 2015, Women's World Champion, World Junior U-20 Champions and rated players can be replaced only from the average rating list. Continental and Zonal qualifiers will be replaced from their respective events, except that in the Zonal Tournament, the replacement must have scored 50% or more in the Zonal event. Otherwise the place passes to the Continental Championship. The average rating list has priority if a player qualifies either from the rating list or a zonal/continental event.
Next step: Add the the 25 events shown on the right side of the chart to my page on the World Chess Championship Zonals.