To randomize the edges of the cells, you can take a Noise Texture node and use it to distort the original texture coordinates.
Since the Voronoi Texture (and others) use Generated texture coordinates by default, they work without the need to plug something into the Vector input. However, to mix in the noise you need to get the Texture Coordinate node as input.
There you can either use the Generated or the Object output (the difference is not too relevant for this question) and mix it with the noise Color output in a Mix RGB node (set to Linear Light for example) which you then plug in the voronoi's Vector socket.
Now you can tweak and experiment with the settings to get a result you like. Scale, Detail, Roughness and Distortion of the noise all have an influence on the outcome and especially the factor in the Mix RGB node, I would suggest you start with a very low value.
Note: Here I used the Object output, if you do this it presumably means you have to change the Scale in the Voronoi Texture to get a similar result as with Generated or none. I also plugged the coordinates into the Noise Texture which is not mandatory. Without, the Noise Texture uses Generated coordinates, it only helps for consistency if both textures use the same coordinate system.