You can try BioMart with all its different options of access (web, APIs, R package on bioconductor). The variation dataset of BioMart allows you to enter a list of Ensembl Gene IDs (you will need to convert to those, if your genes are not already in that format) as filters, than as attributes you can choose variant IDs and phenotype description. You will get the mutations from COSMIC and HGMD plus the SNPs and short indels from dbSNP.
Alternative, you can use the Open Targets batch search tool to get the diseases (pathways, drugs) associated with your genes and from further exploration of the results you can find the mutations (or variants) linking those genes to their associated diseases (such as the skeletal disorders you are interested in).
Since you are familiar with Python, perhaps the Open Targets and programmatic access will be the choice for you: get the diseases and the association scores for your genes depending on the genetic variants (or mutations) they carry. We have a Python client for easier communication with our REST API.
If this is useful but you get stuck along the way, just shout.