To follow up a bit on Mikael's answer, the notion of non-pure shellability is probably more relevant to your situation. Shellable simplicial complexes are wedges of spheres of equal dimension, but non-purity allows different dimensional spheres. You should look at papers by Michelle Wachs and Anders Bjorner if you're interested. However, this will require finding a simplicial decomposition of your space, which may be a challenge.
Added: Since this is now the accepted answer, I figure I should give the precise references. Both papers are on JSTOR (follow the links).
Björner, Anders; Wachs, Michelle L.
Shellable nonpure complexes and posets. I.
Trans. Amer. Math. Soc. 348 (1996), no. 4, 1299–1327. http://www.jstor.org/stable/i311403
Björner, Anders; Wachs, Michelle L. Shellable nonpure complexes and posets. II. Trans. Amer. Math. Soc. 349 (1997), no. 10, 3945–3975. http://www.jstor.org/stable/i311413