How did 無 originate from "a dancer holding something in each hand"?
There might be some confusion as to what the word &quot;borrowed&quot; means. The usage of 「無」 to mean without is a rebus borrowing. From Wikipedia:

An example that illustrates the Rebus principle is the representation of the sentence &quot;I can see you&quot; by using the pictographs of &quot;eye—can—sea—ewe&quot;.

That is, to ask how the sentence

I can see you

originated from the pictures

   

is an incorrect question.

If it is difficult to see how the glyph evolved into its current form 「無」 (Baxter-Sagart OC: /*ma/, without), that is a more tangible query.
Start from a rather vivid picture of a person 「大」 holding a bunch of adornments in each hand, doing a rain dance*.
商甲鐵120.3合集16000
Complexify the adornments, maybe into something highly resembling a sound hint 「某」 (/*məʔ/).
西周金毛伯簋集成4009春秋金寬兒鼎集成2722秦簡10.8睡虎地秦簡隸定　
Omit the shape of the person 「大」.
西漢隸老子・甲馬王堆帛書隸定　
Then finally, abbreviate the bottom of the character into a few dots.
西漢隸25定縣竹簡楷　
Dance is written with the derivative character 「舞」, by adding semantic 「舛」 (picture of two feet).
西周金匽侯銅泡集成11860西漢隸158縱橫家書東漢隸華山廟碑　楷　

*The nature of the dance being linked with rain is from the extensive number of fragments where the character 「無」 is found with the character 「雨」. E.g. 《甲骨文合集》12828: 
 

戊（申）卜今日（奏）（舞）㞢（有）从雨
Divination (卜) on the day of wùshēn (戊申): Today (今日), perform (奏) a dance ritual (舞). Rain appears (有从雨).


References:

漢語多功能字庫
小學堂
國學大師

郭沫若《甲骨文合集》
中國社會科學院考古研究所《殷周金文集成》