What is the small speaker on this antique radio?

Just because the speaker is small doesn't mean it's a tweeter. You'll have to open it up to see what gives. If it's a radio there isn't a way to turn it into bluetooth speaker. If you ever turned it on you could tell what it does- receive am or fm? That won't receive bluetooth. There are bluetooth speakers you might buy and adapt to that home made doohickey, or suggest strongly to your "someone" that they can buy and use a bluetooth speaker as a bluetooth speaker. They might as well be asking you to turn a roller skate into a frisbie.

I believe someone already made some kind of modification to the thing.   

It looks more like an intercom speaker than a radio because it has only on/off and volume.

Regardless the speakers inside will be junk and need to be replaced no doubt.

Open it up,pull out the guts and buy a blue tooth speaker to put inside .

The only way to find out is to open the thing up and look. It could be a tweeter but most likely not since the cover would block and absorb most of the high frequency sound coming out of there. Besides, speakers this old is not going to sound anything close to Hi Fi by today's standards, and if is also a mono audio system, not stereo. 

I believe someone already made some kind of modification to the thing.    

On an antique radio the tuner dial/indicator would have been in that location. Maybe something like this:

https://www.erbzine.com/otr/dial1h3.jpg

So a tweeter could be put there.

What you actually have is a spice rack that maybe some one put a radio in at some point in the past. Which means it could have just been a speaker.

Not being familiar with that model I'd suggest that it'd be a lot quicker to open it up and have a look.  If there's anything at all there then you can tell if it's a speaker or a tweeter by the fact that tweeters don't have air holes in the back of them, speakers do.  If I was tasked with doing that I might rip everything out of it, strip down a bluetooth speaker and put its parts inside that wooden case.  Alternatively if I could get that thing to work as an amp and could find/create a 5V supply then I might use a USB bluetooth receiver and connect it to the amp - with appropriate biasing and maybe a preamp if necessary.  One of those turns any amplifier into a bluetooth amp if you connect it to its input and they're quite cheap.