It is not fully clear to me from your question what kind of mouse gene identifiers you have in hand. Are the NCBI gene ids?
If so, NCBI's homologene can be used to map them to gene ids in human that CMAP can accept.
Alas, at the NCBI web site, this can be done only one-at-a-time.
Enter stage left: Entrez Direct: E-utilities on the UNIX Command Line which below looks up the homologene entry of two NCBI (mouse) gene IDs and outputs a table with two rows for each input geneID, one for each organism, which lists the homologene entry's ID followed by TaxonName and the id in that taxon.
echo -e "15394\n54624" | epost -db gene | elink -target homologene | efetch -format docsum | xtract -pattern DocumentSummary -HGID Id -block HomoloGeneData -match 'TaxName:Mus Musculus' -or 'TaxName:Homo Sapiens' -pfx "\n" -element '&HGID',TaxName,GeneID
5441 Homo sapiens 54623
5441 Mus musculus 54624
4032 Homo sapiens 3198
4032 Mus musculus 15394
Pipe the above into `| grep Homo | cut -f 3`to get just the human gene IDs.
- there is no guarantee on order or results agreeing with order of input .
- if your inputs are other than GeneIDs (such as refseq IDs) you'll have to write some variation on the above.