Try:

@DateTimeFormat($(MyDateParameter),%m/%d/%Y)

See FME Date/Time Functions help for further reference:

https://docs.safe.com/fme/html/FME_Desktop_Documentation/FME_ReadersWriters/!Transformer_Parameters/Date-Time-Functions.htm

@DateTimeFormat($(MyDateParameter),%m/%d/%Y)

Just re-read the bit about this being today's date.   You strictly speaking don't need a Parameter to do this for the Reader Source string.   The above formula could be rewritten as:

@DateTimeFormat(@DateTimeNow,%m/%d/%Y)

So the Source URL can be written to be evaluated as:

http://mywebdatasource.com/date@DateTimeFormat(@DateTimeNow,%m/%d/%Y)

Or whatever URL string parsing is required.

An alternative is to replace the reader with a FeatureReader transformer. You can then start the workspace with a Creator and follow up with a DateTimeStamper (and DateTimeConverter, if necessary) before passing it on to the FeatureReader as a part of the URL.