Christos, if it doesn't have a button, or a hole , then i don't think there is a way to update it without opening it up. If it uses an ATMEL chip (AT90USBXXXX) then , its possible to enter DFU mode by touching 2 pins to ground, its safer to use 2 diodes when doing this ,so not to cross the 2 pins themselves, but bring them both down to ground. Also safer to use a resistor on one of those pins , but if you don't plan on updating frequently, you could do it as 1 time with just wires.
Probably not what you wanted to hear , sorry. I can provide more help if you do manage to open it up , and identify the chip , and maybe post pictures of the board. I could be possible that although there is no reset button installed, the board as the traces which could make updating the chip a bit simpler, although you need to open it. Maybe if it has the traces , you could add the button(s) yourself...
Edit: just saw you posted links to pics, waiting for approval then i'll post more.
Well, the atmega32u2 is definitely upgradable, it believe it is identical to a at90usb162, so the teensy 1.0 .hex should work , just make sure it has the correct crystal (16mhz for original psgroove) if you have a 8mhz , you will have to compile or find a 8mhz version, but thats easy.
I have included on your picture what needs to be done in order to enter DFU mode. The pins DFU and RESET must be connected to ground , and that will reset the mcu , and check the state of the dfu pin , if its grounded , it enters DFU. You can just short them all together , but its not a "safe" idea , you might damage your chip if you do it, if you use the logic i put , the 2 diodes prevent the DFU and RESET pins to be connected directly together.
I have included the .hex , and details on how i got the compiler to use the atmega32u2.
I havent seen behind your board , maybe there is logic similar to what i posted ? Good luck!
Please reply on the functionnality of the .hex i posted , but i repeat , exact same psgroove11 build , that i fixed compiler and changed in makefile to reflect atmega32u2, includes CJPC fix.