Is there a less intense (more causal, less offensive) equivalent single word that means being dishonest in being modest or to show yourself to be modest when, in fact, you are just pretending?
The closest term I can think of is humblebrag, which specifically refers to a statement that appears on the surface to be a sign of humility while actually is a form of bragging. This term is somewhat recent slang and definitely carries a negative connotation.
Stephen Fry: Oh dear. Don’t know what to do at the airport. Huge crowd, but I’ll miss my plane if I stop and do photos … oh dear don’t want to disappoint
If you're okay with using more than one word, I think the closest phrase for a dishonest form of modesty would be false modesty. If you want to be a little more indirect, you can say someone is being ostensibly self-deprecating.
When reading your question, one can't help but think of the word hypocritical:
If you accuse someone of being hypocritical, you mean that they pretend to have qualities, beliefs, or feelings that they do not really have.
Keep in mind that hypocrisy is a very general term that can be used to describe any type of hypocritical behavior. When you're talking about being hypocritical, you just need to specify more precisely in what respect you think somebody is being hypocritical. For example:
John is such a hypocrite when it comes to modesty. He says that he is modest while he is really not.
Depending on what you mean by "modest", coy might work. It's often used to describe someone who is making a big show of being shy and modest, either as a way to flirt or as a way to avoid talking about something sensitive. It can have a slightly negative feel depending on context, but isn't always negative.
- artfully or affectedly shy or reserved; slyly hesitant; coquettish.
- shy; modest.
- showing reluctance, especially when insincere or affected, to reveal one's plans or opinions, make a commitment, or take a stand:
The mayor was coy about his future political aspirations.
Note that in the "flirting" sense it's most often used about women, for good or ill.