Depending on the type of shower you want to install (not the size, but referring to the type of construction), you'd probably have to change the type of drain that is there as well. This might require you to break up some concrete. Then, depending on the type of drain lines, if they are metal, sometimes it's a good idea to replace them anyway. While CI can last a very long time, it might not, and while what you have lasted over 30-years, I'm guessing you'd like the new one to last at least as long...so, depending on what's there, you want to make sure the 'infrastructure' is good to last as well as the new stuff.
Most pre-cast/pre-made pans don't offer the option of placing the drain where ever you want it...you move the drain to where it's needed. A custom, tiled shower pan can have it anywhere, but centered (or end) works best. Yours isn't all that far off, so would still function fine, if (and that's a big if) done right. Lots of ways to build a shower, lots of ways to mess up. It's good you're trying to do some research...keep going.