I have same watch in orange dial which came with their orange rubber strap. I ove the watch but wasn't feeling the orange strap. If you want leather your choices are MANY. I wanted to maintain water resistance/usage so looked for a nice rubber strap. I bought about 4 cheap silicone and PVC bands and they all sucked. Slippery/oily feeling and made my wrist sweat.
After lots of research I came across a number of discussions with people the virtues of the Maratac Elite Composite strap. Some folks said it was better than GEN straps they literally paid well over 10 times more. As such, I bought a Maratac which is EXCELLENT and only $17 delivered off eBay. Hard to describe just how nice the Maratac is on the wrist and watch. They come in black with the standard contrast stitching colors. Your watch would look nice with whitw stitching.
Do a search on the sellers listings to see all the different stitching options.
The other option is a GEN Victorinox strap in black which is available on eBay for $58 in all GEN colors. The Victorinox rubber strap is excellent. However, I don't think they are any better than the Maratac and contrast stitching is not an option.
For some reason I can't post a link to the $17 eBay seller. Do an eBay search on the sellers name: "timepiecerepublic" and then search his store for "Maratac 22 white" to see white stitched straps.
For a GEN strap the eBay seller for $58 is: "magicstrap". He even has one in green similar to the colors you liked in leather.
I'm curious about your watch. I bought the same model about a month ago and it is quite a bit different than yours. My hands are sword hands and other differencdes as well. Is yours an older model?