I'd recommend you to use GowerGower with subsequent hierarchical clustering. Hierarchical clustering remains most flexible and appropriate method in case of small number of objects (such as 64). If your categorical variable is nominal, Gower will internally recode it into dummy variables and base dice similarity (as part of Gower) on them. If your variable is ordinal, you should know that latest version on Gower coefficient can accomodate it, too.
As for numerous indices to determine the "best" number of clusters, most of them exist independently of this or that clustering algorithm. You need not to seek for clustering packages that necessarily incorporate such indices because the latter may exist as separate packages. You leave a range of cluster solutions after a clustering package and then compare those by an index from another package.