There is no danger using a capacitor rated for much higher voltage than you required, nor is there any performance loss for doing so. In fact quite the opposite.
Certainly if you have a DC bias across the capacitors (e.g. decoupling), you want the voltage rating to be much higher than your DC bias, else you need to choose a capacitor with higher capacitance rating than needed. This is because the capacitance of MLCCs drops off significantly as you apply a DC bias.
Most MLCCs don't get anywhere near their rated capacitance at their rated voltage. For an X5R dielectric, typically by the time you get to half the rated voltage, the capacitance has already dropped way below half the rated value. X7R dielectrics fare slightly better - you might expect to still retain 70% rated capacitance by the time you reach half the rated voltage, but even those will drop off.
Most manufacturers don't supply this data, however some including TDK and Murata do give these test results, and you can pretty much expect the same trends to apply to other manufacturers as the technology is practically the same.
As a simple example, this one is a bog standard 10uF 10V X7R MLCC in an 0805 package. At its rated 10V DC bias, the actual capacitance is only 4uF. With a 5V bias it fares slightly better, achieving 7.5uF. In fact you have to be at less than 2V bias (1/5th of the rated voltage) to actually achieve the 10uF capacitance rating. This is shown in the graph below.
This is why you typically want for X7R the rated voltage to be >2x the required DC voltage. For X5R, you probably want to be >4x the required DC voltage. The higher the better.
The only downside for going with a larger rating, is typically the size is required to be larger. However for low capacitance values (sub-100nF), this isn't too much of an issue, and you can easily find high voltage ratings in small packages. For very low capacitances (sub-1nF), you'd probably be hard pressed to find one with a low voltage rating anyway.