This is exactly what I’d do in your situation. If the package didn’t include the jumper wire (which is listed in the package contents on the product page and I believe is supposed to be a fuse of sorts), then the easiest thing to do is probably to just nut the FRONT and TRANS wires together or screw them both to the TRANS terminal for now (if you have confidence that they’re wired correctly in your chime box, then I’d label them for easier reconnecting and/or Chime Controller wiring later), and you can obviously use the included Wi-Fi Chime for the doorbell sound.
Depending on the Cam models you’re using, you might be able to use some of those as accessory chimes. That’s another option to consider while waiting for Wyze’s Chime Controller stock to replenish. Chime Controller was still available (but listed as “Sold Out”) when I checked in the app ~10 days ago, but the last several times I’ve tried to look it up, it hasn’t shown up in the app shop at all. I’ve never seen it available for separate sale via the shop on their Web site, which has been disappointing and perplexing to me (and that’s something else I’ve shared with employees, along with the frustrations @carverofchoice expressed).
I’ve also seen mention of at least one Forum member buying a refurbished Video Doorbell v2 just to get the Chime Controller, so that’s another potential option if you want to get your mechanical chime back into service sooner.
If it were me, though, I think I’d figure out an alternate chime solution (Wi-Fi Chime, Cameras as Chime), bypass the mechanical chime (for now) and plan to get a Chime Controller when they’re available again.
Welcome to the Forum, @samuelchodur! 