Is it possible to design a band-pass filter with fewer taps than a series HPF + LPF?
Assuming that your legacy FIR linear phase filters were designed using windowing method, then yes, you can combine those two FIR linear phase filters into a single FIR linear phase filter and it will be shorter than the the serial cascade. 

However, you won't be convolving the individual impulse responses to get it. Rather, you should use a multi-band windowed FIR filter design technique. An example of how to do it can be found on Alan Oppenheim's DTSP book on chapter 7 filter design section. 

Specifically he makes use of Kaiser window design approach acording to which the filter (window) length is empricially dependent on the transition band width and peak approximation error. 

So, given the same transition band width and error ripples of a HPF -> LPF cacade, whose lengths are M samples each, you would be using a single multiband filter of length M with the same transition band and error ripple.

Note that as MattL also indicates, you may also chose different filter types to achieve similar respones, but that depends on what you want to achieve finally.