One hink pink for Santa's cut facial hair would be Santa's sheared beard.
boot loot
shelf elf
spare hair
fair hair
big wig
hair care
shag wag
care bear
pig's wig
Thin inn is the hink pink for skinny hotel.
A hink pink for a giant mermaid could be "big wig." Hink pinks are typically rhyming pairs of words that describe something, and in this case, "big" refers to the giant aspect while "wig" playfully captures the idea of a mermaid's flowing hair.
The hink pink for "boy's test" is "lad's quiz."