Looking for advice

I have a workshop that has an old Technics receiver in it. I mainly use it to listen to the ball game while working (yes, I’m that old lol). I also have a fire pit outside near the workshop where I stream music from my phone onto a small portable BT speaker. But I would also like to listen to the game out there (games are only broadcasted on FM signal due to contractual issues between team & radio station). I would like to find a cheap way to consolidate what I’m doing. I was thinking of hardwiring outdoor speakers to the outside of the workshop and connecting a BT transmitter to the receiver. I think that’ll allow me to play the game from the receivers FM signal outside or stream music from my phone to the transmitter, then out to the speakers. Does this sound plausible? Any thoughts or suggestions (keeping in mind I’m trying to do this cheaply)? Thanks in advance 

Yes that’ll work. Depending on the sound quality (and quantity- volume!) you want you may even be able to use a small portable BT speaker. My wife got one cheap, Coleman, rubberized and in camo it looked like absolute crap until she turned it on and the damn thing actually sounds pretty good- and darn near indestructible! She got it on some deal, you could probably find something similar around $50. No hardwire, take it wherever you want it. Plenty good for listening to games. Heck you could play music, just not loud.
i got my wife a refurbished oontz angle bt speaker on ebay for around $20--sounds really good for the price w/long battery life. a bt transmitter can be had for $15 or so.