LocalSend looks great, but I don't think it captures OP's intention. It would require someone else to download the app if they wanted to receive a file, but OP is asking for something that uses the already existing Airdrop/Quick Share so that they could send a file to someone without them having to install anything. I've had similar wants, as when I've wanted to share something with someone in public that I don't really know, I've just had to upload it to send.vis.ee, but that can be quite slow and inefficient. Something leveraging both Airdrop/Quick Share (that doesn't require you to be connected to the same WiFi network like LocalSend) would be ideal, as those are features included by default on stock iOS and Android (no install required). For instance, there was something similar called WarpShare that allowed you to share something via Airdrop from an Android device to an Apple device (but only in that direction), but its development has stalled and it isn't capable of using Quick Share for Android devices.

I'll take a look at that. Thanks