Okay, I'll take this out of the comments and put in an answer for all of us to work on.
To directly answer your question:
"Is there an estimate for the percentage of these genes whose primary
function is related to regulation of gene expression?"
It depends on how you define "gene expression." And what cellular processes you want to include in that definition.
Larry's answer is the usual standard response, especially for people (such as me, ha) that have spent significant time studying transcription factors. About 1% of human genes have DNA binding domains and are thought to be directly involved in regulating the transcription of genes into mRNA - these are transcription factors (TFs). Closely related are cofactors, which regulate expression by binding to TFs or RNA polymerase machinery, but not directly to DNA.
Regulation of gene expression could also include modifications at the chromatin level - here you would include chromatin remodelers, histone acetylases, deacetylases, methylases and the histones themselves.
mRNA transcripts can also be regulated by miRNAs: post-transcriptional regulators that bind to complementary sequences on target mRNAs, which leads to translational repression or target degradation and gene silencing. So you would also include the proteins involved in this process, most notably the RNA-induced silencing complex, which includes Dicer.
There are also proteins involved in mRNA stabilization and turnover, which effects gene expression.
I'm not sure if anyone has added up all of the genes above to determine an overall percentage of the genome.
If you include in your definition of "gene regulation" post-transcriptional modification, folding chaperones, intra-cellular transport, extra-cellular and intra-cellular signaling, and so on - then Shigeta is right, you begin approaching 100%. In the most basic sense, life itself is gene regulation.