If one gets dressed initially with the proper order of shirt before bottoms, then if one changes the shirt, does one have to get completely undressed and then redressed or is it ok to just change the shirt?
The idea of getting dressed in a specific order is not mentioned in halacha, however there were gedolim that removed the clothing of the lower part of their body first, in order to take their tzitzis off later. This is an idea, not a halacha, and it definitely doesn’t apply to women. Other then that there is no need to be concerned. The only idea brought in halacha is that when we dress we put the right side on first and when undressing we take off the left side first, as a form of showing prominence for the right side. Also regarding tying our shoes, since we tie tefillin on our left arm, therefore we the left shoe before the right one.
PIskei Teshuvos 2-5.