Does a player need to offer a cut when shuffling something other than their deck, such as when playing Marnie?
Yes. The purpose of a cut is to reduce the opportunity for cheating; that applies anytime a player is randomizing their cards.
Source: TPCi Rules Team (2020-02-06)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH1_169
SWSH1_169
SWSH1_200
SWSH1_200
SWSH1_208
SWSH1_208