What should a person who suffers from intermittent urinary incontinence do when they leave the house, given that the private part becomes soiled after using a tissue, and it is difficult to clean due to the lack of sufficient water? Is it permissible for him to clean the private part with a wet tissue and pray in his current state always, due to the hardship?

If the impurity has spread beyond the usual exit, then washing with water is obligatory to purify the area. As for the past, there is no obligation to repeat the prayers that were performed in that state due to ignorance of the ruling. However, if the impurity has not spread, wiping with a tissue or similar item is sufficient, provided it is dry and not made of religiously revered or forbidden materials. The best and most preferable method is washing with water.