How shall I put this? While no doubt a fun AU it's not very plausible...
For a start the Incas rose to prominence relatively late. In the 12th century AD they were a minor city state centered on Cusco, and they only really started expanding beyond that in the 1430s. Nowhere near enough time to come to dominate
all of South America before the Spanish arrived.
Then there's the ability of anyone to fully conquer and control all of South America... it may not be impossible but given the shear variety of landscape (including lots of jungle and some rather nasty mountains) it's not terribly plausible particularly when your only large domesticated animal won't carry more than 30kg. It's no coincidence that the extent of the Incan Empire in the real world corresponded rather closely to the normal habitat of Llamas and related species.
Add to that in the real world you had natives in Patagonia holding off the Spanish (and later Argentina and Chile) until the mid-19th century; and there's still good chunks of the Amazon with uncontacted tribes even today.
Even giving total dominance of South America as a freebie, having it hold together when you split it into sub-Kingdoms... not gonna happen. Sooner rather than later one or more of the Kings will decide they should be Emperor instead of the Emperor and chaos will soon follow...
Pyramids... While not unknown in South America, proper Pyramids (rather than earthworks or terraces) were not really an Inca thing... some earlier cultures from the coast of modern Peru built Pyramids, but it's more of a Central than South American thing. Hell!
The temple to the Incas' chief god Inti in their capital Cusco didn't feature a pyramid. There is no reason to suppose any continuing Inca empire would get hung up on Pyramids to the extent of compromising the utility of shipping. Probably should google Incan religion before drawing any more of their ships
Of cause, if you did want to try a plausible take there's a few options:
1. Pizzaro initially attempted to keep the Incan Empire going as a puppet state. Between infighting between the conquistadors and the would-be puppet ruler, Manco Inca, escaping and trying to establish a new Incan kingdom on the upper fringes of the Amazon that fell to pieces. If Pizzaro was to have a falling out with Charles V, or if Manco Inca could play his cards right during the chaos (50,000 Inca warriors suddenly turning up on one side or other of the conflict between the Pizzaro brothers and Diego de Almagro?) then you could see the independence of the Incan Empire restored and a more modern state evolving from there. And with the wealth of silver in what is nowdays Bolivia...
2. A class of mixed Incan-Spanish descent remained major land-holders (though locked out of much political power) well into the 1700s, and continued to maintain major aspects of Inca culture, including use of Incan regalia, up until the rebellion of
Tupac Amaru II was put down in the 1780s. Have a successful similar rebellion, say, a century before. Well, a restored "Incan" empire probably isn't as interesting as something with solid continuity to the real thing...