Welcome to the Forums!!
First off, I am required to tell you this:
you don't need all the wonders. You don't need most of them. Heck, you don't
need any of them. They make nice trophies, but overall they're
mostly just big wastes of shields and take away from your ability to play the game at even middle-difficulties. If you are playing for a culture win, by all means build away. If you want any other victory, build them selectively (like Sun Tzus or Leo's Workshop because their effects last forever and have unlimited applicability... compared to the relatively useless Oracle, for instance).
That said, if you are still interested in "catching them all," there is an option in the game to have the computer alert you anytime another civ begins construction on a wonder. F7 shows you which wonders are being built and in which city, as long as you have contact with the civ that is building it. Other than that, the only way you'll be able to tell how close a wonder is to its completion is to investigate the city via espionage.
If that sounds too pricey, just run a few dozen units over to the city and burn it to the ground. Then the AI will be back to square one. Or wait for the AI to build it, then capture the city and the wonder
Think of it this way... the Pyramids will take 400 shields to build. 400 shields will *also* get you 20 archers, or about 14 swordmen or horsemen, if those are available. Imagine the damage you can do with 14 swords/horsemen or 20 archers
Now imagine if you skipped building the Oracle, the Pyramids, the GLighthouse, the GLibrary, the GWall, the Colossus, and the Hanging Gardens. That, my friend, will get you around 70 swordmen or horsemen. You could, literally, take over the entire world with that many units in the AA