Firstly, im sorry for your loss.
Only you know the depth of your relationship & what impact this will have on your exams.
If it happened within a couple/few weeks of exams you likely have a good chance the university will allow you to use resit examinations in the summer as your first attempt, depending on the uni’s policy.
Generally unis have fairly strict policies on this (and may require evidence) because without such a process unfortunately some people do abuse the EC system. Id check your university handbook or website for details & if you want to go down this route speak to your tutor.
I would generally say delaying your examinations will make life tougher as you’ll have to use your summer going through them all so you won’t get a nice break from your studies, however if you feel you won’t be able to prepare for the exams whilst your grieving then that is also understandable.