I can see why you feel there might be fringes visible in the 1938 photo, but I think it is the dress fabric which creates that effect.
If there were fringes and if the two brooch are the same as I think they are, then the fringes should be visible at the bottom of the brooch in the 1950 photo - but none can be seen.
I am going to go out on a limb and ask if this could be the Koh-i-noor.
Roberts says that QEQM had a new brooch setting made for the diamond. In the centre of this brooch is one large diamond. Whether the stone looks large enough to be the Koh-i-noor is difficult for me to judge.
Another factor we should keep in mind when trying to evaluate this jewel is that the Koh-i-noor was slightly recut for QEQM's crown and with a new setting it would look different from how it looked on Queens Victoria, Alexandra and Mary.