Allah, The Glorious says in Quran (9:28) : إنّما المشركون نَجَس INNAMA ALMUSHRIKOON NAJAS. Verily the polytheists are impure. This a Quranic fact which all Muslims should follow.
Those who participate in Muharram believe and love Imam Husain (AS) being a divine leader of Truth, which means that they are not really polytheists even if their families are been classified as non Muslims. Their noble act in commemorating Imam Husain (AS)'s martyrdom reflects their undeclared faith in his values.
Allah Knows what is in the hearts and the acts usually reflect what is in the heart. That is why we take the acts who love Imam Hussain (AS) as an indication of their faith in him and his faith which is Tawheed.
This is allowed unless doing so would be considered as a type of disrespect or mocking for Muharram which is highly unlikely. Also provided that one doesn't swim somewhere where the environment could be haram
There would not be any shar'i problem with changing places, as long as there is no intention in desecrating the sanctity of this holy time of mourning.
It would be advisable, if it is possible, to postpone until after Ashura, and to continue to allocate time for your 'azaa` and dedication in mourning for Imam Husain (a.s.).
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