Can I use part of a song without the author's consent in a video about war?

Yes, you can, if your video belongs to a mixture - a composite work that is the result of a creative selection and arrangement of short excerpts of other legally published musical or audiovisual works without harming their protection, resulting in a complete object, the parts of which united by the creative intention of the author of this work and if you specify the name of the author and the source of borrowing.

This is regulated by Article 22 of the Law of Ukraine "On Copyright and Related Rights": Without the permission of the copyright holders and free of charge, but with the indication of the author's name and the source of borrowing, it is allowed to use legitimately published literary, artistic, musical and other works to create a potpourri based on them, a work in the genre of parody, a work in the genre of caricature.

Please also note that the free use of works is provided that the work used has been lawfully published, and the restrictions will not harm other normal uses of such work and will not unreasonably limit the legitimate interests of the respective copyright holders.