Both the mini circuits and the thorlabs filters are designed for 50 ohm inputs, they will probably not work well with a 10x probe. But you shouldn't be using a 10x probe if you want low noise measurement of low frequency signals anyway. The thorlabs ones are meant to drive a high impedance output like a scope and will work correctly with a 1X probe. The minicircuits ones are 50 ohm output. They will still probably work on a 1 Mohm input, but they will have different bandwidth from the data sheet. Alternately, use 50 ohm mode on your scope or a tee and a 50 ohm terminator.
I suspect you won't get the advantage you are hoping for in any case. On mV level signals, the noise of the scope front end and ADC are a big source of the noise.
A filter in front of the scope won't reduce those, only noise present on the input signal. Scope BW limit and digital filtering can average out noise from the source as well as from the scope analog front end. If your signal itself has a lot of high frequency noise, then the filter will help. But averaging on the scope will get the same effect for $0.