No dedicated "remote" exists for PSP 1000 game control. It uses built-in controls (D-pad, face buttons, analog nub, shoulder buttons).
Use PSTV (PlayStation TV) — plays PSP/Vita/PS1 games via HDMI with DualShock 3/4. Or PPSSPP on PC/Phone + Bluetooth controller.
No game-controlling remote for original PSP 1000.