You seem to have decided now anyway but for what it's worth - YABU.
You don't have an appointment, so you don't need to WFH. In my workplace (I manage a team), if a colleague wants to switch their WFH day or work an extra day from home, they'll just ask - no lies needed - and once they are a responsible, capable colleague, as (nearly) all my team are, I'll have no issue saying yes.
If you don't feel you can do likewise, and that the company policy is no WFH unless in that specific circumstance, then (morally, as you keep referring to) you are wrong to do it. You are also not approaching your workplace or employer with integrity.
You also are not just planning on a trip to the beach in your lunchhour, you plan to stay longer, then work in a local cafe. I wouldn't be remotely happy, and it is against our WFH policy, very clearly, for my team to work from cafes. So if you are doing this, and your employer wouldn't agree, again, it's a poor decision and YABU.