Here's what I would do...
Go to
http://www.cardomain.com
Search for other 1993 Nissan Sunny owners. See if you can email or somehow contact them and ask for advice. I know I saw a couple on there with the same dash as you... with after market radios installed. So they should know what to do.
Here's an example...
http://www.cardomain.com/ride/717519/2
Nico is a fantastic resource, but we just have so few Sunny owners.. you won't find a ton of help here... yet! But, if people like you stick around, we can continue to grow and improve NICO.
BTW... If I had to guess on how to remove it... I would guess that they have a few screws holding it on the bottom under the steering wheel. Also, perhaps a couple screws just above the gauges on the bottom of the visor. Then there are most likely multiple pressure clips that are holding it in. I used to own a Sentra... that's how it was... there were a couple screws hidden from view on the underneath surface areas, but most of the dash was clips. Just pull hard.. not hard enough to crack the plastic or anything.. but hard enough to release those clips.