We no longer produce any clock alarms which operate on battery mode simply because batteries are not a reliable source for alarm activation ...
Fairly recently I've seen line powered clock radios that included a "standby" battery that would keep the clock running until time for the alarm to go off if the line power failed. Something of this kind wouldn't be advertised as battery powered, but if they're still making anything of the sort finding the battery and clipping in a little bit bigger battery (in parallel with the one intended) could solve your problem if you can stand a little bit of ugly from the extra leads.
A clock radio with a digital display probably has a "main bus" inside that's at a typical battery voltage and would use less battery power if you can find the right place to hook in. The ones with "hands" would normally require a motor of some sort that might drain the battery a little faster.
The specs on ones I've seen some time ago indicated that the battery should last "up to 6 hours" if line power fails, but of course two of the same kind in parallel should give you at least 12(?), and you could probably use rechargeables and refresh them from the cig lighter accessory plug in your vehicle or some other handy source.
Of course this is only a viable approach if you feel the urge to tinker with such stuff with uncertain probabilities of success.