Substitute for a Standing Mixer using a paddle
A paddle mixes denser ingredients vs a wisk attachment that will aerate light ingredients. Things mixed with a paddle are always intended to be completely mixed- as opposed to folding or cutting which aren't done with a mixer.

This means that you can use whatever you want to thoroughly mix those ingredients (as long as it doesn't melt them): a stand mixer, a hand mixer, a spoon, etc.

Most hand held mixers have much smaller motors than most stand mixers. They can't handle stiff doughs and you can destroy your mixer, stripping the gears or burning out the motor, if you attempt to overdrive it. Better quality hand mixers can handle almost anything a stand mixer can.

That said- any hand mixer should be able to handle cream cheese and mayo with no problem.

TL;DR

Go ahead. Your hand mixer should be able to handle those ingredients just fine without spoiling the recipe or damaging your mixer.