Cable carrying digital signals has to have characteristic impedance matched to source output impedance and DACs input impedance (all three the same), otherwise there will be possible reflections on impedance boundaries. Such reflection can produce time jitter of the signal that will result in added noise after D/A conversion. Characteristic impedance for high frequency signals is roughly SQRT(L/C) of the cable (independent of length) and for unbalanced DAC connection is usually set at 75ohm (110ohm for balanced input). Ideal cable would be at least 1.5m - even better 2m. It is to make first reflection from the end of the cable miss edge of the signal without adding to it (distorting it). It is possible, that your analog cable impedance is very close, but chances of that are slim. Digital cable doesn't have to be expensive since impedance match is most important (cheaper cable can be a better match).
The only case when cable doesn't matter is when it is extremely short (no reflections). If you can make any cable shorter that 1 foot (6" would be even better), then you don't have to worry about impedance. It is also possible that your DAC has strong jitter rejection and will sound the same (inaudible jitter).
