WetGeek I can continue looking for another keyboard that might work with both.
Well, that didn't take long. I decided to try the Logitech version that I'd looked at before, and almost bought it first. The deciding factor was that it isn't rechargeable, and I'd come to appreciate that feature in the two keyboards I've been using. However, it runs on two AAA batteries that are said to last for two years, so that may not be such a big issue.
It pairs with up to 3 devices using three channels of Bluetooth 3.0, which should be all that's needed for a keyboard, and that should work just fine for both the HP and the Dell.
And a big plus is that it provides two separate full-size keys for the up and down arrows, so that's one less thing I'd need to get used to. Unfortunately, it won't be here today. Not until next Wednesday. But I've been swapping between two keyboards for years now, so a few more days won't be a big deal.
The cost of the BT5.1 keyboard was too little to bother returning it. I'll give it to my granddaughter for switching among her various devices, so it will get a lot of good use.