114 should be fine, in fact you'll probably need to cut a couple of links off when you fit it to the bike anyway.
Chains shipped to work are always 116 links, and I don't think I've ever cut any fewer than four links off when fitting to a bike. Except when I had to join three chains for the HPV!
Fitting tip: Place bike right-way-up, whether it's on a workstand, hanging from a clothesline/tree branch/whatever, or leaning against a wall. Set derailleurs to small chainring and small rear sprocket. Feed chain over gears & through derailleurs, ensuring correct chain orientation.
Shimano 7900/6700/5700/4600 series chains are directional; feed the open-ended outer link forward over the front ring, and ensure that the solid outer link plates (engraved with model ID) are facing outward (i.e. towards you when you're looking at the bike from the drive side, which is where you're working from). With the chain fed through and the ends held in each hand, pull them together, then overlap them, so you form a reasonably straight line from the bottom of the chainring to the rear derailleur. Keep pulling tension with your left hand until the "free" chain is not dragging on the wrap of chain over the upper jockey wheel. (In this position, the rear derailleur's spring tension pulls it back so the jockey wheels are one behind the other, rather than below.) Adjust your chain overlap so the open end in your right hand aligns with a matching link in your left, and there is a 5-10 millimetre gap between the free chain & the jockey wheel. Cut the chain at your selected link so you have a closed end, then pin the chain with the supplied pin.
If you prefer to use a quick link, you will also need to remove the open-end link after you have measured the chain length.
This method will work with the widest available gear range (because there is enough travel designed into the rear derailleur to take the chain slack) for your component set, triple, compact double or standard double + 11-28 (or even 30 & 32t cassettes now!as long as you have a compatible derailleur) without having to think about your specific gears. It also means you can swap cassettes around without worrying if your chain will be long enough (although you may need to pull a couple of links out if you change down to a compact crankset, or put a couple in if you change up from a compact to a standard).
That should about cover it.