Methane has 2 problems: 1. it's a massive greenhouse gas if it leaks, 2. it requires CO2 to make, and in a decarbonized future that can only come from either biomass (limited) or DAC (expensive).
You would either want ammonia or methanol. Ammonia does not have any of these problems, but it's very toxic. Methanol has the CO2 problem as well, but it's a liquid, so it's easier to transport. Neither is perfect, but there are no perfect solutions.
Methane is the worst of all options. If you want a hydrocarbon, then usually methanol is what you want. And don't trust me on that, just look at what projects are actually planned out there. Plenty of green ammonia and green methanol projects, green methane is exotic at best, barely anyone wants to do that.
Ammonia is a greenhouse gas itself, and it tends to react with air creating various nitrous oxides, that are much more potent greenhouse gases than methane, very toxic, and create acid rain (after what it becomes fertilizer).
The best shipping option is probably just to face all the issues and ship the hydrogen. But storage is a different matter.
What you likely mean is that when taking atmospheric CO2, burning methane does not cause additional CO2 emissions. However, that is orthogonal to the problem of methane itself as a greenhouse gas when it leaks (which by all experience it does regularly).
https://acp.copernicus.org/articles/22/9349/2022/
> "It is, however, very likely that hydrogen is emitted throughout the value chain, but it is unclear – given lack of data – which components contribute most and least to emissions."
Synthesis of methane from water-sourced hydrogen and atmosphere-sourced CO2 is at present a good deal more expensive than fossil natural gas, but that's a somewhat artificial situation: natural gas production is heavily subsidized and many of the costs are externalized to the public (see global warming, air and water pollution, etc.). However, once accomplished you can just feed this renewable methane into the existing natural gas infrastructure, and get the hydrogen back as needed from well-understood processes, i.e. steam-methane reforming.