UniProt most certainly has an API: all of its resources are RESTful (look for the links on any protein page) and there are tools such as UniProtJAPI.

I'm not sure what you mean by a BLAST API, but it's possible to run remote BLAST programatically. See for example Bio::Tools::Run::RemoteBlast for Bioperl.

However, I think you are a little unclear about exactly what you want to do and how to do it. If I had protein GIs and wanted to do pairwise comparison using BLAST I would:

1. Use the GIs to retrieve protein sequences in FASTA format via Batch Entrez
2. Download and install BLAST locally
3. Create a local BLAST database from the sequences using makeblastdb
4. Run blastp using the FASTA format file as query against my local BLAST database

In that way I would generate identity/e-values for every sequence vs. every other sequence.

You can do it with bioperl.

Get the sequences with the efetch module: http://www.bioperl.org/wiki/HOWTO:EUtilities_Cookbook

Align the sequences with the simple align module: http://www.bioperl.org/wiki/HOWTO:AlignIO_and_SimpleAlign

edit*

Just as a side note, if you do use blast to do your alignment, I wouldn't use the e-value for that output. Blast E-values are normalized p-values to the search space of the database. Since the search space is essentially length of sequence A * length of sequence B, the e-value is probably not the best metric as short sequences would artificial give high e-values. I would use the bitscore instead. Also remember that the lengths used to calculate identity in normal blast includes gaps.