Praise be to Allah.
We have stated previously that health insurance is a kind of commercial insurance and it is not permissible to deal with it, except when a person is forced and compelled to take it or there is a pressing need for it, because of what it involves of ambiguity and gambling. Please see the answer to question no. 170654
In the answer to question no. 22373 we stated that there is nothing wrong with keeping cats unless there is the fear that they may cause harm, such as if they are sick or if there is the fear that they may transmit disease and so on, because of the general meaning of the words of the Prophet (blessings and peace of Allah be upon him): “There should be neither harming nor reciprocating harm.” Narrated by Ibn Maajah, 2340; classed as saheeh by al-Albaani in Saheeh Ibn Maajah.
With regard to excessive care in looking after cats, paying excessive attention to them and spending large amounts of money to look after them, this is a waste of money and a focus on things that are of no benefit in religious or worldly terms.
Rather than grieving over a cat that is suffering this problem, we should grieve over what is befalling the Muslims and their children in all places; rather than wasting money on a cat, we should spend it in charity for the needy among the Muslims.
Whatever the case, there is nothing in what you have mentioned to suggest that there is any necessity or need to take out haraam insurance; rather we think that this excessive care and expense comes under the heading of wasting money, as stated above. Because keeping the cat in the condition that you mentioned carries the potential of harm for you and your family members, you should get rid of this cat.
You could send it to one of the animal care charities that are widespread in your country, and they will look after it.
If that option is not available, then let it go and leave it in the street or a public place, and Allah will take care of it according to His will.
See also the answer to question no. 7004.
And Allah knows best.