How to design a feed line for a single wire antenna
Your output is unbalanced i.e. single ended so you need a monopole for simplicity. A monopole needs a ground plane and the better the ground plane the more effective it is. This is why you sometimes see this on the right: -



The four extra wires run parallel with ground (usually) and, through a mixture of being the right length and their capacitance to real ground give a decent result. Those wires connect to the outer on the coax.

But, if your monopole is close to the PCB it will work reasonable. After all a walkie talkie only uses a monopole and relies on "person" capacitance to ground to make it effective.

However, if you don't have a ground plane on your PCB you will need one.

Antennas don't necessarily need a ground plane to produce a radio wave - Voyager 1 and 2 managed quite nicely without one because their antenna doesn't rely on a ground plane. Neither does a dipole antenna but that needs a balanced drive.

Just try it and see is my advice but do use a GP on your PCB for this and EMC reasons.