Electronic – Are there data connectors designed to fit through small round holes

I'm familiar with pin headers, but I have trouble finding a connector type where a 4-lead connector can fit through a 4 mm round hole.

The standard pin headers with a pitch of 2 mm and 2.54 mm are too large, a 2×2 pin connector has a diagonal larger than 4 mm.

The next smallest type, 1.27 mm, would barely fit through and might get stuck in the 4 mm hole.

The next smallest type, 1 mm, would fit, but I couldn't find long enough male pins to reach the top of the casing my PCB is inserted in (pin headers of larger sizes have plenty of "double decker" variants)

So my question is, are there any other connector types (possibly) unrelated to pin headers, which could fit through a 4 mm round hole?

Notes:

To not make this into an X-Y problem, here is my original problem I would like to solve:
A central device is connected to multiple smaller devices, to each with a 4-lead connection (5 V, very few mA). I would like to find a connector, so that for example the male is soldered to the PCB of the central unit, and the females are soldered on cables which are coming from the smaller external devices (or the other way around, with the females on the PCB). However, each cable, with the connector mounted on it, has to fit through a 4 mm diameter round hole, this hole is not on or near the central device. The ideal solution would be for the cables to be plugged into the top of the central unit, this is why I considered a "double decker" pin header, with appropriate square holes on the top of the casing.

A much less optimal solution would be to have holes on the side of the casing, so the pin headers or sockets on the PCB would be angled 90°.

This is when I started thinking: maybe there are completely different connector types which I never heard about, which would solve my problem much better.

I though of audio jacks, there exist some in 4-lead variants, but the plastic casing is much thicker. Also, they are expensive compared with the pin strips.

the problem with most very thin multi-leaded connectors (used in laptop computers, for example), is that although they are very thin, they are also very wide, they are not designed to fit through round holes.