I ride to work, and ride around clients all day so minimum 1 hour each way on the commute, anything up to another 4 hours going around although that's rare. The only way to remedy the sweating is showering, so I probably have 5 showers a day (I have a shower at my office and several of my clients have showers).
Take a change of clothes with you to work every day, arrive early, and have a wash. If you don't have a shower, find somewhere nearby that does have one and will allow you to use it. Be courteous, buy your own soap and bring your own towel (I used to leave a towel at work before we put in the shower.). Many places such as engineering workshop or even gyms have showers. I used to go to the mechanics next door to my office and use theirs.
Always try and make sure you are fresh after a bike ride, finish your shower with cold water, and take your time under it, this cools down your muscles, because if you just got off a bike and have a shower, your internal heat can easily start you sweating again if you don't do this.
I have never found it impossible to find a shower nearby. Admittedly I'm in the tropics and being third world no one would bat an eyelid if I jumped in a river with a bar of soap, (I have one client a two hour ride away with no shower, but there's a stream nearby) but even when I was in NZ I used to make sure to have a shower, just because you can't smell it doesn't mean everyone else can't.
The key thing is it's your decision to bike... don't make it someone else's problem.