The allowance you reffer to is mentioned as a hetter concerning the acceptance not to sing as a zecher lichurban. Ever.
There are specific instances where it applies and where it does not. See Shulchan Aruch o'ch 560 siff 3 and mishna berurah 13. Seemingly working in an office would be more comparable to a sheppard singing, or a woman doing her housework, which would not be allowed, only situations like the dockworkers and cattle workers was allowed in the gemara, as their singing actually helped them work and it was not just for pleasure.
To apply any of these laws to Sefira, and the three weeks for that matter, is a chidush, but it seems the minhag of most people is to only keep those laws about music during these two periods. There may be proof for this 'minhag' found in hilchos sefira siman 493 m.b. #3, where he mentions that during Sefira 'certainly one should not engage in dancing for pleasure'. This statement is hard to understand unless we assume as we did that the music laws were misappropriated from being a general constant law, and taken to apply only during certain times. But note that in the Shar Hatzion he brings a Pri Migadim who is unsure if one can engage in such behavior during the entire Sefira, not just the half he keeps! Not like what the minhag seems to be. So the minhag to apply the issur to music is a confused and confusing one.
The issur for music during sefira is not clear, but it is practiced. The hetter you mention probably would not apply to your case. However as noted you might not need a hetter:)
This is the info. Now take this to your L.O.R. and see what he has to say. Don't forget to let the community here know.