Using your sentence structure, only 'persuade ' is correct. You can't use 'urge' within that sentence structure, it isn't correct to say 'managed to urge me.' You could however say 'The salesman urged me to buy a new printer as a well as a computer.' There is a difference in meaning between them. In my example sentence using 'urged', it isn't known if you did buy a printer, just that the salesman tried to convince you to buy one. More information is needed to know whether they were successful or not. However 'managed to persuade me' show that you did decide to buy a printer as well the computer. You were 'persuaded' to do what the salesman wanted.

They're not the same but very similar. Just a difference of importance. Persuasion is trying to get someone to do something in a friendly, constructive way. I might try and persuade you to learn Chinese for example. Urge has urgency, where I am strongly trying to persuade you to do something, usually for an important reason. I might urge you to wear a crash helmet on a motorbike for example. Also, i've not heard of the Oksford dictionary, you may have meant Oxford?