Why not 这个笔是谁的?
why no measure word is needed ? 这(支)笔是谁的？Is it for phonetic reason (zhe zhi) or anything else ?
The classifier is not needed at the beginning as long as the object is indicated next to 谁的, which is the pen 笔.
The sentence you proposed is also correct.
Duo accept 这笔是谁的！