Database migration script
There's no reason why you can't modify the data retrived from MySQL and still insert multiple rows at once into PostgreSQL, for example something like this:

fields = '''
customer_id customer_name contact_name address city postal_code country
'''.split()

cur_msql.execute("SELECT {} FROM mysqlcustomers".format(','.join(fields)))

rows = []
for row in cur_msql:
    if row['customer_name'] == NULL:
        row['customer_name'] = row['contact_name']
    rows.append(row)

params = '({})'.format(','.join('%s' for _ in fields))
query = "INSERT INTO psqlcustomers ({}) VALUES {}".format(
    ','.join(fields), ','.join(params for _ in rows))

cur_psql.execute(query, rows)