It is a difficult one. But you are right that 'willen' is changing the use of 'weten' Because u use two verbs, you only conjugate one and you are a bit flexible with the other.

When u use 'willen' you always have to use something else. You want something. In this case you want to know a result. 

In your example: hij wil het resultaat van zijn examen weten / hij wil weten wat het resultaat van zijn examen is. In the first option there is a little bit more focus on the result and in the second on the wanting to know something. But both are usefull and natural.

But instead of 'weten' you can use for example 'lopen/ walking': Hij wil naar de supermarkt lopen / Hij wil lopend naar de supermarkt (there is more focus now on the way he goes to the supermarkt and in the first case there is a bit more focus on going to the supermarkt. But both are usefull).

Or 'koken/ cooking': hij wil voor zijn vrienden koken / hij wil koken voor zijn vrienden. (first a bit more focus on the friends and more natural. the second on the cooking. But both usefull and natural)

Because you use 'willen', you can put 'weten' or 'lopen' on different places. "willen' is conjugated in this case and you only conjugate one.

When you for example skip the 'willen', you only have one choice for the verb 'weten': Hij weet het resultaat van zijn examen/ Hij loopt naar de supermarkt/ hij kookt voor zijn vrienden

Now there is only one verb and you need to conjugate this. You can only use this verb now on one spot.

But as you see it is not only with 'willen' but everytime with two verbs you can use the second one more flexilbe:

Hij gaat volgend jaar reizen door Europa/ Hij gaat volgend jaar door Europa reizen.

But sometimes you also change the meaning a bit, so be carefull with changing the place of the verbs.