Which kind of flip-flop not require the CLK

This sounds like an application for an S/R latch.

Why would a clock input make it more stable? Do you even have a clock signal?

Latches and flip-flops are different devices, and appropriate for different applications. Both have the drawback that they are not suitable in applications where the other would be better.

It may help to know that SR latches aren't really used much anymore. If your system needs one, you can easily build it from a dual NOR gate or a dual NAND gate (depending if you need active low or active high inputs). For example, the SN74AUP2G02 could be used to make this latch:

NOR latch mage from: https://www.allaboutcircuits.com/textbook/digital/chpt-10/s-r-latch/ 

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You can do the same thing with a D-type Flip-Flop as long as it has an asynchronous preset and clear pin (or set / reset... same thing).

When used in this manner, the D and CLK inputs are left unused (terminate to GND or VCC).

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It's also important to note that latches don't have a default output state -- you must force them into the state you want at system startup. [FAQ] What is the default output of a latched device? (Flip-Flop, latch, register)