There are no scuba police. You are free to dive any way you want. The card just allows you to buy air and get on a charter boat. The card does not guarantee your safety. What's you dive buddy going to use? You weren't planning on relying on their computer, right? Are they going to want to do tables?
What amazes me is that you got an SDI certificate without doing the SDI program. There is something seriously wrong with this picture. Did you take the SDI written exam? As SDI really likes computers, they actually teach something about them. I don't know about SSI but PADI doesn't mention them at all.
There's nothing wrong with diving to the tables. In fact, you are probably a lot safer just because of the built-in round-ups and the fact that you are not watching a clock telling you when you are up against your multi-level NDL. You actually plan the dive in advance and dive with a square profile. There's a lot of comfort in diving this way.
I'm still coming to grips with using a computer. Intuitively, I don't like it. In the back of my mind the adjusted NDLs are running around. They should be on my slate. Unfortunately, I quit doing that when I gave up my BC and moved to a BP/W. No pocket for the dive table and slate. Well, that and old age keeps me from reading the things underwater anyway. They're hard enough to read in broad daylight.
You need a good dive timer. Unfortunately, the best is probably the Uwatec. There's one on eBay right now Item # 380110274150 but new, they cost about $125 including shipping from Spain. They may be popular with tech divers but they seem hard to find in the US. Maybe I just missed them. That, and ScubaPro doesn't authorize online sales in the US.
Many (but not all) computers can operate in gauge mode. Tech divers tend to use them that way because they work their own decompression profiles. But it doesn't save any money to buy a full blown computer and just use it as a depth gauge and timer. Still, it allows you to work with the tables.
The problem with a wrist watch with rotating bezel is forgetting to set the bezel at the start of the dive. then you have to remember when you terminated the dive. All in, workable; but a PITA. I have never tried the stopwatch feature of a digital watch. It might work ok if the numbers are large enough.
But depth and time are going to be very important if you plan to use the tables.
Richard