It's possible.
Whether it's worth the effort, or not, is up to you.
Google "Mk1 Honda Jazz din conversion" and you'll find the replacement dashboard facia you need (assuming you don't plan on just butchering the OEM panel) for about £40.
Just had the stereo out of mine and it's not as straightforward as Youtube would have you believe.
Technically, it is just a case of one screw to remove the cover from the bottom of the heater controls and then 2 more screws inside the bottom of the facia panel but the screws are bloodyhard to reach and the heater cables mean the panel doesn't want to move very far.
I found it helped to remove the glove box interior and then disconnect the white/yellow heater cables from the heater so they're loose, which'll give you a lot more wiggle-room to move the facia panel around and undo all the screws that attach the heater controls to it.
If you decide to buy the facia panel with the standard DIN hole in it, let me know and I can talk you through pulling it all to bits in greater detail.