Use x10 probe instead of x1. Those with selectable switches, glue or tape it in the x10 position. x1 is very rarely needed IMHO, and it's frustrating whenever your probe has accidentally changed to a x1 probe and your voltage values are 10 times off.
If you still have too much capacitance, the options are:
A cheap DIY "lo-z" probe
https://www.eevblog.com/forum/projects/lo-z-probe/which trades lower HF AC impedance for higher DC resistance,
Or an expensive active probe which has a tiny FET amplifier in it.
Cases where the 10-20pF of capacitance would
kill a circuit are very rare, though. It's likely you did something else which killed your soldering station. Ground loop, for example. Or shorting two adjacent pins with the tip.