Energy usage for compression is tiny compared to actually transiting, and you can get some of the energy back. Or if it was hydrogen fueled, just run your engines for a short time.
But yeah, simply running a compressor powered by hydrogen should suffice. I assume the airships would require some surplus hydrogen anyway, in case there's a mid-flight leak or something.
The corollary pipe dream here is to line the entire interior of the envelope as a fuel cell membrane and use the airship as a portable battery.