The Answer
No, there is not. The word shenanigans has no singular form. It is a plurale tantum (plural: pluralia tantum), which is Latin for plural only.
Words like clothes, scissors, glasses, and pants only exist as plurals. There is no such thing as a clothe, a scissor, a glass (unless you’re talking about a drinking vessel), or a pant.
Many of these pluralia tantum are types of clothing, including pyjamas, shorts, and tights. Even more of these words refer to tools that work with our eyes or ears (e.g. goggles, binoculars, headphones, earmuffs). It makes some sense that many of these are singular items that go on both of our eyes/ears/legs. When talking about a certain number of these items, you only ever say a pair or pairs.
There are also a number of two-part tools that are only ever plural, like scissors, pliers, and tweezers.
We can say “give me a pair of scissors,” but not “give me a scissor.” True, there is a sense in which scissors are two objects, two blades, being used as one tool, and many similar tools are also pluralia tantum: pliers, tongs, tweezers, forceps. But not all such tools are plural. A clamp, a bear trap, and a flat iron are also tools made of two joined parts, and they are singular.
It appears as though there are some patterns regarding when words are pluralia tantum. Many words regarding ownership can only be plural, such as your belongings, valuables, or riches. Nouns that describe feelings work in a similar way. You can have the blues, the jitters, or the doldrums, but much to my dismay you cannot have a single heebie-jeebie. Descriptive terms for activities are plural more often than not, like shenanigans or heroics.
The word annal means “a record of events of a particular year” according to dictionary.com, but the plural annals is much more common.
You may think that academic areas of study, like economics, physics, and linguistics are only ever plural, but they are actually used as singular nouns. For example, “Economics is the social science that studies the production, distribution, and consumption of goods and services”.
And what words are pluralia tantum varies between languages.
Pluralia tantum vary arbitrarily between languages. For example, in Swedish, a pair of scissors is just en sax (literal translation “one scissor”), not a plurale tantum; similarly, in French, a pair of trousers is ‘un pantalon’.
There is also such thing as singularia tantum, a word that only has a singular form, like water, bread, and hair.