You can say:
Put your pride aside.
Put aside your pride.
that will fit the meaning you want to convey perfectly which is, in other words, according to Longman Dictionary:
To try to stop thinking about a problem, argument, or disagreement, because you want to achieve something.
They have provided a similar example where they used "pride":
You must put aside your pride and apologise to him.
Notice that "apologise" is British English. "Apologize" is the American one.
And although the construction put [something] aside exists in English, I don't find it works properly (semantically) with "shyness" as it is not a matter of refusing to do that particular action because of the desire of achieving something else.
The case with pride fits the definition as the person doesn't want to apologize since s/he wants to satisfy their pride, preserve it, and not disparage it.
Whereas with "shyness", it is an obstacle for the person himself/herself that stops them from achieving or doing whatever presented at that moment.
I suggest you say instead:
Overcome your shyness.
Get past your shyness.