One hand = katate
Grab = toraeru (tori)
Try "toru", "to take".
Japanese will often change the syllable of the second word for easier pronunciation. i.e. flower = hana, ikibana is flower arranging. 'h' changes to 'b' since they are related in hiragana their phonetic alphabet. Same with 'to' and 'do'.
I asked my Japanese friends and they say they just know.
There are a few rules of thumb. Katate-dori uses "-dori" because "katate-tori" would be difficult to say at natural speed even for native speakers. Unvoiced syllables often become voiced following a syllable made up of an unvoiced syllable, and retain their usual sound when following a voiced syllable. They also often become voiced following the "-n" sound. And I believe intonation plays a role, as well, as it makes some combinations easier (or harder) to say than others. There are many exceptions, though.