@Anirbhan,
You are thinking too much. First of all, having very minimal knowledge of astrology – you are judging things much. Before recommending anything, I think about all the effects and only then I recommend.
Ketu is neutral to Mercury. There is no harm to your ascendant or to yourself. Ketu is being harmful if you wear his gemstone you will be neutralizing his effects by showing more dearness to him.
In other words, if you want to build friendship with your enemy what you are going to do? Gift them their loved things / which they like, to please them – Am I right?
Even all the remedies works on the same natural phenomenon. And more over Mars is position in 3rd house where I can see you are more quarrelsome with your younger sister. Good to know that you are showing some concerns about her. There won’t be any harm for your sister. Its just a medicine, if you take medicine to your ill health will that going to cure your sister’s ill health? No, right. Hence no problem to your younger sister she will be alright.
I can see due to these malefic planets and due to the extreme effect of ketu you are thinking more about vairagya / reluctant to any good things of life.
And please remove from your mind that if you wear the gemstones, then you are going to get cured in just minutes. All these remedies just to remove the negative effects pertaining to that planet and to add some good possible energies pertaining to that planet.
If you are still not happy in wearing Cats Eye. You can do some other remedy for Ketu.
GOD BLESS!!!
Srinivasa Temkar