(1). Some experts tell me that Laudenbach's paper is incomplete and contains gaps.

(2). The result you seek can be  deduced in the following papers by Lizhen Qin (disclaimer: he was my student):

*On moduli spaces and CW structures arising from Morse theory on Hilbert manifolds.* J. Topol. Anal. 2 (2010), no. 4, 469–526

*An application of topological equivalence to Morse theory.* 
arXiv:1102.2838