PS2 Wireless: Translates Bluetooth/2.4GHz → USB HID or PS2 proprietary wireless protocol. PS1 has no USB, no Bluetooth stack, no driver for the dongle.
Real Solutions for Wireless PS1
PS1 Wireless Adapters (RetroBit, 8BitDo, Brook): Plug into PS1 controller port; pair with modern Bluetooth controllers (8BitDo, DualShock 4, Xbox, Switch Pro) or included 2.4GHz pad.