To understand what this means, you need to look at what is said before the line about "requisite decency." If you do that, you will find that the young many was hoping that he could find a decent person. The person would have to be decent enough to buy his story about how he got lost.
In the line you cite, the young man is said to be hoping that Gortsby has close to the "requisite decency." The word "requisite" means something like "required" or "needed." "Decency" refers to the lines I mentioned before where the young man hopes for a person decent enough to believe him. So the "requisite decency" simply means enough decency (or gullibility) to believe his story.
The actual wording in the story is as follows:
"...one could go to one's Consul and get the requisite help from him....Unless i can find some decent chap to swallow my story and lend me some money I seem likely to spend the night on the Embankment."
This little memorized and pre-rehearsed speech is intended to suggest that the con man belongs to the class of people who are accustomed to foreign travel and that he has been to schools like Eton and Oxford, where the expression "decent chap" would be more likely to be heard than elsewhere. A "decent chap" would probably be an upper-class type, one who would do the right thing by an equally decent chap who happened to be in trouble. By suggesting that he himself is a member of the upper class and that he is a "decent chap," the con man strongly implies that he has plenty of money and will surely repay a small loan. He is also challenging Gortsby to show that he too is a "decent chap." If Gortsby is a decent chap, he may develop a friendship with the pseudo-aristocrat, who has told him he doesn't know a soul in London and who would therefore be glad to have a knowledgeable Londoner like Gortsby as an acquaintance.
When Gortsby punctures the con man's story by pointing out that he doesn't have a cake of soap to prove his story, he is dismissing the idea of establishing any kind of relationship with him. But then when Gortsby finds a cake of soap near the bench, he realizes, among other things, that he has failed to behave like a "decent chap" and rushes after the con man to make amends.
Gortsby is not represented as a gentleman of leisure. Saki tells us that "Money troubles did not press on him," but that hardly means that he is rich. He works in an office and is relaxing on a park bench before going back to his small flat. He and the young con man are probably about equal in education and social status, but the con man is putting on an act. Actually, the con man is putting on two acts simultaneously. He is pretending to belong to the upper class and at the same time pretending to believe that Gortsby is his social equal. Gortsby snaps at the bait. He says:
"Not at all impossible," said Gortsby judicially; "I remember doing exactly the same thing once in a foreign capital, and on that occasion there were two of us, which made it more remarkable...."
Gortsby has probably only been out of England one time in his life, but he is trying to put himself on the same plane as the other man. In Gortsby's misadventure he did not go to his Consul but:
Luckily we remembered that the hotel was on a sort of canal, and when we struck the canal we were able to find our way back to the hotel."