Switching from 118 link chain to 114 link chain - problematic or no big deal?
Sometimes the length as provided (114, 116, 118) happens to be the exact length needed, but the norm is to size it down by removing some number of links.
The optimal length is determined by the size of your big back gear, your big chainring, and your chainstay length, with some length added on top of the minimum those factors will allow depending on the derailleur in question. If you go too short you can break your rear derailleur, derailleur hanger, chain, and/or or frame by shifting into a gear combination that overextends the rear derailleur.
Nine-speed trekking bikes can be outliers for chain length. The usual scenario for this is a 48t large chainring, 34t or 36t cog, and long chainstays, i.e. 450mm+. That bike setup being a mainstream entry in some regions is basically the biggest reason 118 link chains even exist. It's very possible you can't get away with 114.
Kindly request to buy a cut-off segment of new 9-speed chain from a bike shop plus two two-piece master links to splice it in, or Shimano pins if it's a Shimano chain and segment and if you're confident with that. (More finicky). It's not pretty but will be fine. In practice the SRAM and KMC two-piece links work with whatever 9-speed chain (except Campy) without issue, don't worry about that part.