Hi.
I'd like to make my own near field probes. So, instead of building the complete probe + BNC cable, I came up with the idea of extending my Siglent SD1102X probes with a custom adapter.
That doesn't solve for your actual requirement, though (there are plenty of uses for the tip-to-BNC adapter, of course, but specifically for the requirement you mention of a near-field probe).
If you have to buy that, then you may as well just buy the right parts (if you want to DIY the probe, that is), which will be a ready-made BNC cable with thin, flexible coax and a ready-made short, semi-rigid SMA cable with the same connector as you have on the end of the flexible cable. All should be available on Amazon, eBay etc.
The response won't be flat or calibrated, but that's often not important at all versus just seeing activity. Once you have the parts, there are many online resources showing you how to solder the loop.
The attached photo shows typical example parts (you won't need all, and it depends on what you buy). You can see a longer, thin, flexible coax cable to attach to the 'scope. The short blue cable happens to be semi-rigid, and it could be cut in half. The other two items are adapters, if required, to get the flexible cable attached to the semi-rigid cable.
Just a personal choice, if it were me, I'd go for the PCB-based approach (nothing invalid with the plain coax approach of course; that's just as effective). You don't even need to design it; there are
existing H-field probe designs. The Gerber files are downloadable from there, all ready for uploading to any PCB manufacturer's website.
Using that PCB requires a side-mount SMA connector and then a thin, flexible BNC cable (with SMA on the other end), and then that's it. If you can't find a BNC-to-SMA cable, then you'd go for the SMA-to-SMA cable, and use an example BNC adapter like the one in the attached photo.