Is it safe to use a water pump without a ground wire?
Alright.  Your first problem is the "cheap and unmarked" part -- two prong appliances can be safe, but only if they are "double insulated" or Class II.  Such an appliance will have a square-within-a-square symbol on its model number label, alongside any testing marks that may have been applied.

Since this pump of yours lacks any independent equipment testing, labeling, or listing, I wouldn't trust it to not shock you any further than I could kick it.  A dedicated residual current device/ground fault interrupter designed for personnel protection (i.e. 5mA trip threshold, nominal, with trip timing as per UL943 Class A or your country's equivalent standard) would be highly recommended in this application; even if the pump does try to zap you, the RCD/GFI would trip and cut off the current before a serious shock could take place.

Also, next time -- please don't get the cheapest pump you find at the bottom of the barrel!  Cheap, unlabeled crap is cheap, unlabeled crap because of the safety-compromising shortcuts that are taken during design and manufacture.