We present medium-resolution K-band long-slit spectroscopy of 29 true, likely, possible, and candidate Galactic Plane planetary nebulae (PNe) from the UWISH2 survey, many of which have only been recently discovered. These objects are bright in molecular hydrogen (H2) emission, and many have bipolar morphologies. Through the detection of the Br{gamma} emission line, which traces ionized hydrogen, we find that the majority of the candidate PNe are indeed likely to be PNe, while 2 of the targets are more likely young stellar objects (YSOs) or pre-planetary nebulae (pPNe). We detect Br{gamma} in 13 objects which have no detection in IPHAS or SHS H{alpha} surveys. This implies that they are potential members of the little-known optically obscured PN population, hidden from wide-field optical surveys. We use the spatial extent of the H2 1-0S(1) and Br{gamma} lines to estimate the evolutionary stage of our targets, and find that W-BPNe (bipolar PNe with pinched waist morphologies) are likely to be younger objects, while R-BPNe (bipolar PNe with large ring structures) are more evolved. We use line ratios to trace the excitation mechanism of the H2, and find the 1-0S(1)/2-1S(1) and 1-0S(1)/Br{gamma} ratios are higher for R-BPNe, implying the H2 is thermally excited. However, in W-BPNe, these ratios are lower, and so UV-fluorescence may be contributing to the excitation of H2.