What I am saying is connect D13 to the shift register SRCLK pin
D11 (MOSI) to the Serial Data In pin
Connect D8 to the RCLK (latch) pin
D10 is then used as CS/latch to the radio, and
D8 is the latch for the shift register
(although if it is 74HC595 type, it is really the output register clock)
SRCLR connects to +5, OE/ connects to GND, or to a control pin if you need to use it as output enable.
Connect a 0.1uF cap from shift register's VCC pin to Gnd.
Then only 1 more pin is used, and not 3 more to use shiftOut( )