DECLARE @v TABLE (x VARCHAR(50))
INSERT INTO @v VALUES
-- list of strings that column will be updated with
('37845840'),('34879335'),('33879336'),('37855840');
 
DECLARE cursor1 CURSOR FOR SELECT <TABLE_ID> FROM <SOME_TABLE>;
DECLARE @id INT;
 
OPEN cursor1 FETCH NEXT FROM cursor1 INTO @id 
 
WHILE @@FETCH_STATUS=0
BEGIN
  UPDATE <SOME_TABLE> SET <UPDATED_COLUMN> =
    ( SELECT x FROM
       ( SELECT *, ROW_NUMBER()OVER(ORDER BY x ASC)rn FROM @v s ) a
         WHERE rn=CAST(rand() * (SELECT COUNT(*) FROM @v) AS INT)+1 
    )
  WHERE <TABLE_ID>=@id 
  FETCH NEXT FROM cursor1 INTO @id;
END 
 
CLOSE cursor1
DEALLOCATE cursor1