The spelling with the l sound is "shalln't". Also, I came across this after I heard it in Stargate SG1.
Season 9 - Episode 4 "The Ties that Bind". About 25 minutes in.
Daniel Jackson is told something along the lines of "we shall have to get used to each other". And he replies "No, we shalln't".
Also, iOS autocorrect will automatically punctuate "shalln't" for you.
Answer from Fogmeister on Stack Exchange"'ll+not" = "shan't"? | WordReference Forums
Can I use “shall”, “shan’t”, “whilst”, and “henceforth”?
Does anyone know why "shan't" doesn't have another apostrophe ("sha'n't"), since it's missing letters in two different spots? We have multiple apostrophes in words like "couldn't've".
Are there any contractions that we no longer use?
Videos
As a non-native English speaker, I was taught all these words above and I can even use them naturally. “Shall” being similar to “must” or “Will”, “shan’t” being the abbreviation for “shall not”, “whilst” meaning “while” and “henceforth” meaning “from now on” or “from that time forward”. Though, I’ve seen some videos where native speakers deem them old-fashioned and out of use and say they’re not appropriate to use in modern English. Is that true but only in speech? What about formal compositions? Are they perfectly valid today?
*As I am writing this, words like “amongst”, “midst”, “amidst”, “against” that have the same -st suffix pattern with “whilst” came to my mind.