Here's where, in your shoes, I'd be wishing I hung out with dodgy people so I could buy a fake or stolen blue badge to use.
Meanwhile, I'm probably teaching my grandmother to suck eggs, but I'll take the risk, even if just as a reminder of what you already know.
With places like hotels and shops, some will make arrangements for a suitable 'unofficial disability parking space' when you show them you genuinely need one. You can phrase it as "I don't currently have a blue badge, but I'm disabled and I'm wondering what reasonable adjustments you can make for my needs, because I don't want to cause problems with my wheelchair blocking spaces or denting anything."