Rather than use default Open file function, you just open the file through add-in.
 
I've tested simple script like below to convert "case_id" to nominal, for 2 TSV files inside 1 folder.
Pls mind the path that I set is "Documents/TSV".
You can change the path for testing at your PC.
If all good, then you can convert this JSL script to add-in (refer to https://community.jmp.com/t5/Learning-Center/Add-In-Builder/ta-p/276711 )
 
Hope it helps.
//Open  Table to pick file
Names Default To Here( 1 );
file = Pick File(
	"Select the TSV file to input",
	"$DOCUMENTS/TSV",
	{"All Files|*"},
	1,
	0
);
If( file != "",
	dt1 = Open(
		file,
		Import Settings(
		End Of Line( CRLF, CR, LF ),
		End Of Field( Tab, CSV( 0 ) ),
		Strip Quotes( 0 ),
		Use Apostrophe as Quotation Mark( 0 ),
		Use Regional Settings( 0 ),
		Scan Whole File( 1 ),
		Treat empty columns as numeric( 0 ),
		CompressNumericColumns( 0 ),
		CompressCharacterColumns( 0 ),
		CompressAllowListCheck( 0 ),
		Labels( 1 ),
		Column Names Start( 1 ),
		First Named Column( 1 ),
		Data Starts( 2 ),
		Lines To Read( "All" ),
		Year Rule( "20xx" )
		)
	)
);
//Standardize "case_ID" to character nominal
Names Default To Here( 1 );
dt1 :case_id << Data Type( Character ) <<
Set Modeling Type( "Nominal" );