He wants to go for Hajj but he gets a few drops coming out after he urinates and it is too hard for him to wash his clothes

Praise be to Allah.

Firstly: 

What comes out after urinating is usually wadiy, which is a thick white liquid that comes out in white drops. It is naajis and invalidates wudoo’. 

Al-Nawawi (may Allaah have mercy on him) said, explaining the differences between madhiy and wadiy: As for madhiy, it is a thin, sticky white liquid that is emitted with or without desire; it does not gush out and it is not followed by tiredness, and one may not be aware that it is being emitted. Both men and women experience this. 

As for wadiy, it is a thick, white, cloudy liquid that resembles maniy in its thickness, but it is different in its cloudiness and it has no smell. It comes out immediately after urinating, or when carrying heavy objects, and it comes out one or two drops at a time, and so on. The scholars are unanimously agreed that ghusl is not required when madhiy and wadiy are emitted. End quote from al-Majmoo’ (2/160). 

Shaykh Ibn Jibreen (may Allaah preserve him) was asked: When I finish urinating, I see some maniy-like liquid coming out, and I do not know whether I have to do ghusl every time I urinate or what should I do? Because I am not sure whether its effects are the same as the effects of intercourse. 

He replied: 

This “maniy” that comes out after urinating is the well known “wadiy”. Because it comes out after urinating and it flows easily it does not necessitate ghusl, rather it only invalidates wudoo’, so you have to wash the penis after that and do wudoo’, but you do not have to do ghusl. Ghusl is only required when maniy is emitted in spurts and with feelings of pleasure, otherwise it is not required. Spurts means when it gushes out forcefully, not like urine which flows out or comes out in drops. So it does not matter if it comes out like that. End quote from Fataawa Islamiyyah (1/226). 

See also the answer to question no. 47693. 

Secondly: 

So long as these drops only come out after urinating, then it is not like urinary incontinence in which urine comes out constantly and the person has no control over it. In that case you should get ready to pray before the time for the prayer begins, so that you will have enough time for these drops to stop. You should keep a piece of cloth or a handkerchief with you to prevent this najaasah from spreading to your clothes. Then you will only need to change this cloth, and this will be easier for you than washing your clothes or changing them. 

If you forget to put the cloth, or the najaasah spreads to your clothes, and it is too hard for you to wash them or change them for some reason, then we hope that there will be no blame on you if you pray in them. 

Shaykh Ibn Baaz (may Allaah have mercy on him) said: The person who is suffering from urinary incontinence and has not been successfully treated has to do wudoo’ for every prayer after the time for it begins. He should wash off whatever has gotten onto his body, and he should set aside clean clothes for praying in, if that will not cause too much difficulty, otherwise he is forgiven, because Allaah says (interpretation of the meaning): “and [Allaah] has not laid upon you in religion any hardship”[al-Hajj 22:78] and “Allaah intends for you ease, and He does not want to make things difficult for you” [al-Baqarah 2:185]. And the Prophet (peace and blessings of Allaah be upon him) said: “When I command you to do a thing, do as much of it as you can.” He should take precautions to prevent the urine from spreading on his clothes or body or the place where he is praying. End quote from Fataawa Islamiyyah (1/192). 

It is not permissible for you to pray when these drops are coming out so long as you know that they will stop, even if that leads to you missing the time of praying in congregation. 

The scholars of the Standing Committee were asked: There is a man who has urinary incontinence, which appears for a while after he urinates, but if he waits until the incontinence ceases the prayer in congregation will have ended. What is the ruling?  

They replied: If he knows that the incontinence will end, it is not permissible  for him to pray in that state, seeking the virtue of praying in congregation. Rather he has to wait until it stops, then wash his private part (instinja’) and do wudoo’, and offer his prayer even if he misses the prayer in congregation. He should hasten to clean his private part and do wudoo’ after the time for prayer begins, in the hope that he will be able to pray in congregation. End quote. 

Fataawa al-Lajnah al-Daa’imah (5/408) 

Thirdly: 

With regard to doing Hajj on behalf of your brother this year or next year after being treated, see which is easier for you, and it does not matter if you delay doing Hajj on his behalf until next year. 

And Allaah knows best.