The impedance of coax relies upon the inner and outer diameters being constant. It's best not to pinch any coax but especially if it's used to transmit or reception is critical it really needs to stay round.
More technical stuff. In this the diagram the 'εr' stands for the dielectric constant, which varies depending on the material used.
Take a typical coax, RG-58/U. This has an inner conductor O.D. of 0.036", which is the same as the dielectric I.D. (Di), and the dielectric O.D. (Do) is 0.116". With a solid polyethylene dielectric constant of 2.25 this gives your characteristic impedance of roughly 50Ω (calculates to 46.8Ω). With the shield and outer insulation thicknesses the overall O.D. will be 0.195".
For the sake of argument say you pinch the coax so it's outside is 5/32" (0.15625"). The inner conductor and shield are unlikely to compress being copper and tin. So it'll be a little bit of the outer jacket but mostly the dielectric that distorts. So say the dielectric becomes 0.07725" in O.D. now. The impedance at that pinch be calculated and will be about 30.5Ω.
With that a lot of other stuff can be found. Reflection coefficient can then be calculated, that will be 0.25. With this you can estimate VSWR, that's going to be 1.67. Other things can be estimated, mismatch loss for a reflection coefficient of 0.25 is 0.28 dB. Return loss will be 12 dB, which means about 6.25% of the transmitter power is reflected back due to this example pinch.
If you need coax to go through narrow spots you can use a smaller in diameter coax, such as RG-316. There's a downside in distributed loss, meaning to avoid a mismatch in impedance (it'll remain a constant 50Ω) the cable has higher loss (at UHF this is substantial). So you'd want to especially keep it short. There are some antenna mounts that mix coax types, a short length of RG-316 at the end to get behind a seal that then transitions to RG-58 or RG-8X for the length inside the vehicle.