If bluetooth capability is a deal breaker for you, I'm afraid it's going to be the bottleneck as far as throughput goes. On my MBP, the default streaming codec is AAC with a 256kbps target variable bit rate, and can be coaxed into using 320kbps CBR. This means that anything you play over bluetooth is going to have the resolution of iTunes Plus or Apple Music files.
AAC is a lossy codec, so this means that the fidelity to whatever master it was encoded from is always going to be worse. (Unless you have a lossless file, in which case it would be comparable).
There are few ways to get around this. High-rate bulk data transfer is just not what bluetooth was intended for. If you have ever used bluetooth handsfree headsets or your car's handsfree connection for calls, you know what SBC sounds like, which is what the bluetooth audio stack falls back on if your device doesn't support AAC.
I get the sense that you are partial to Sony products, their solution for playing high-resolution audio wirelessly is LDAC. It's a codec with more efficient encoding and compression schemes that allows for up to 96kHz/24bit audio to be transferred over bluetooth. It's also a lossy codec (by necessity) which means that the 96/24 audio you receive is an approximation of the 96/24 source.
Unfortunately, this is moot in the current situation of Apple not supporting LDAC /Sony not licensing LDAC for software implementation — except for Android.
The most likely reason for this is LDAC's competitor, aptX. It's the same basic concept: more compression, better algorithms for encoding audio to send more of it over bluetooth. aptX is on most recent android devices, but not on iOS. It is on macOS, though, and if your headphones/speakers support the codec, and the configuration process goes without a hitch, it should be used automatically.
So you have a Mac, which has aptX and BT, but no LDAC, Sony headsets with LDAC and BT, but no aptX, and a Sony walkman, which, if you have a bluetooth capable model, supports LDAC and BT, but NOT when it is being used as a DAC. (Sony doesn't license LDAC for/sell DACs which can transmit its output through bluetooth, since it would effectively be a <more popular codec> to LDAC converter.)
At the moment, it looks like you'll have to load up your walkman with any dsd files if you want to listen to them in a higher resolution format than what most music streaming services provide.