How can I legally land VFR in class D airspace with low and few clouds? This question is a bit specific because it applies to an actual situation I'm observing for a flight I'm looking to make tomorrow.

I'm a Non-IFR rated pilot looking to fly class D airspace. My destination airport is anticipated to have clouds (FEW @ 1,000 ft). In this case, it seems like it would be pretty easy for 1 single cloud's position to make it impossible for me to land at the airport despite being able to (likely) safely land. For example, if the cloud were over the middle of the runway, but I had plenty of runway at my landing end, it's technically possible that the requirements for distance from clouds could keep me from landing here.



I realize the example is trite, but hopefully this illustrates my point.


What is the appropriate way to handle this situation as a pilot? 
I'm calling up tower before I have a visual on the airport (which would be the case in this situation) would they likely deny clearance to land due to knowing that a singular cloud sits out there and would cause a bust the visual flight rules or might they clear me without regard to the rules?
What is considered cloud clearance in this situation? I realize clearance is easy to determine if you are directly above, below or adjacent to a cloud, but more commonly you'll be at some sort of angle to the cloud as in the picture. Shown are two ways to consider cloud clearance (in red and blue lines)
What is the appropriate way to handle this situation as a pilot?
  


First, tell tower about the problem.  They may be able to assign you a different runway, have you loiter (circle) for a minute or three, etc.  It's likely not the first time this has ever happened.

If necessary ask the tower for a Special VFR clearance.  That changes your cloud clearance requirements dramatically in your favor.  Note that the tower is not allowed to offer this clearance to you - you have to explicitly ask for it.


  
  I'm calling up tower before I have a visual on the airport (which would be the case in this situation) would they likely deny clearance to land due to knowing that a singular cloud sits out there and would cause a bust the visual flight rules or might they clear me without regard to the rules?
  


J. Hougaard answered this part in the comments - the tower is likely not checking how far you are from a single cloud.