It is clear that Islam prescribes burial, not cremation.
You may to opt for burial, if this is not encouraged but permitted in the religion of your relatives (you did not say what other religion you mean).
If this is excluded, you might also assist cremation. The following Hadit implies that Allah may forgive you in this case.
The Prophet (ﷺ) said, "Amongst the people preceding your age, there
was a man whom Allah had given a lot of money. While he was in his
death-bed, he called his sons and said, 'What type of father have I
been to you? They replied, 'You have been a good father.' He said, 'I
have never done a single good deed; so when I die, burn me, crush my
body, and scatter the resulting ashes on a windy day.' His sons did
accordingly, but Allah gathered his particles and asked (him), 'What
made you do so?' He replied, "Fear of you.' So Allah bestowed His
Mercy upon him. (forgave him).
P.S. Muslim are allowed to assist a non-Muslim funeral and it's unusual to bury a non-Muslim according to the prescriptions of Islam.
P.P.S. I have added the last sentence according to my education and our practise, where we are mostly attending or assisting the funeral of Christians which are to a larger part compatible with Islam. This fatwa treats the subject, in conclusion confirming that we may attend and support the funeral but not fulfill rites that contradict Islam. It also confirms that we are not supposed to give a Muslim funeral to a non-Muslim.