I'm not going to give you concrete recommendations, but instead I would prefer to leave some comments.
Let's start with the "full sized stage keyboard". I suppose that you mean 88 keys, and DS6.5 (octave distance of 6.5 inches), which I call the "Procrustes piano"
. The site Pianists for Alternatively Sized Keyboards
resume the problem very well: if everyone plays the same size, most are playing the wrong size! And why 88 keys? Bösendorfer builds a 97 keys acoustic piano, and MIDI has 128 notes. But if your music doesn't need the extreme octaves, perhaps an instrument with 61 or 73 keys would be enough, and you would have more options to choose.
Latency, when talking about MIDI music production, is the time that elapses from when a note event is generated, until the sound is actually produced. The contribution of the MIDI controller, MIDI cables (or MIDI USB) to the overall latency is usually negligible compared to the main issue: the audio buffers size. The main contributor is usually the synthesizer, because producing or processing digital audio always require some amount of data buffers. To reduce the latency, you need to reduce the buffers size. One extreme example of this is the "Microsoft GS Wavetable Synth" included in all versions of Windows OS, with big latency and without any way of reducing the buffer size; avoid it like the plague. Software layers between the synthesizer and the audio interface hardware also contribute to the overall latency (DAW, mixer, effects, ...) Some (cheap) consumer audio interfaces require large buffers, and also the operating system drivers, but you may find laptops with good audio interfaces. If not, you may need to purchase a professional audio interface (or a new laptop).