A solution that can be implemented in a short time and doesn't require too much maintenance is the UCSC Tracks Hubs.

Basically, you create your (big)Wig files and store them to a webserver. Then, people will be able to access to the tracks from any other UCSC browser installation (e.g. the one at UCSC), by adding a parameter to the URL. See this example of a UCSC Hub: http://genome.ucsc.edu/cgi-bin/hgTracks?db=hg19&hubUrl=http://vizhub.wustl.edu/VizHub/RoadmapRelease3.txt

This solution is quick and easy, and you do not have to setup and configure a custom UCSC instance. Moreover, people will be able to use it from any other browser installation, and and compare it with their own datasets. However, I don't know exactly what you mean by "integrating the browser in your web service", and which type of web services you are developing, so I am not sure if this is useful for you.

P.s. even if you do not use track Hubs, have a look at the Track Hubs Database Definition document, which I think is the best documentation available for defining tracks in UCSC.

I have never tried it myself but I came across this http://genomewiki.ucsc.edu/index.php/Main_Page.

There is detailed instructions to mirror UCSC browser.

Hope this helps