The info in the datasheet is probably not clear because "you should not need to know this". Based on looking at this and other family datasheets it seems as if the difference between the W and non-W version is the power fail voltage level. Both chips seem to be ok with 6V on any pin so I suspect they both work on 5V but the W version should not be used in a 5V environment because of the power fail level being so low. This is just a guess from looking at the datasheets so it is your choice to try it. I would probably pop it into my Xeltek or Unisite and program it that way but if I did not have either, I would try programming as a 5V part.
Alternately, if you are worried, you could try the Arduino driving SRAM method I mentioned to Rogerio on this thread. In that case you could drive it at 3.3V.
I ran into a similar won't work problem with one of my HP 16xx logic analyzers and its LAN interface. Turns out if the MAC address is not programmed in Flash (battery died in a timekeeping device), the LAN interface will not come up at all. I just programmed in a typical value for an HP device (random MAC) and it came right up. Guess this is the same as your problem.