One of the big advantages of using Scrum is that it makes true progress visible. By having a definition of 'done' and by looking to have a potentially releasable increment at the end of each sprint the progress of the team is very transparent.
If you have UAT outside of the sprints then progress will be unclear.
As an example, say the team has 5 stories done at the end of the sprint. A few weeks later when the stories went through UAT some serious problems were found and the team had do a lot of rework. It is clear that in these circumstances "5 stories done at the end of the sprint" has little meaning.
My recommendation would be to try and do UAT as a part of your sprints. This can be a challenge, but it is usually possible.
One thing that helps is to get a commitment from your Product Owner that they will be available for a certain amount of time during the sprint.
Another thing that can help is to have pre-booked 'slots' in the Product Owner's calendar when they know they will receive stories to be tested. For example, one team I worked with had a 2-hour slot in the Product Owners calendar every week on a Tuesday. The Product Owner new to keep that time free as they would be expected to do UAT during that time.