Walking them around your house should be no problem as far as disease and parasites are concerned.
Most of the those that they could pick up outside your house you are likely tracking in on your shoes anyway. Sniffing and rubbing against your outside shoes is like reading the newspaper for indoor cats.
In this regard, they are already exposed to most of the risks.
Since they are already three years old and have never been outside, I would advise against unsupervised outside exploration.
They are already past the age where they learn quickly, lack experience in survival outside, and get themselves in all kinds of dangerous situations simply because they will panic easily.
Ideally you would walk them on a leash, it may take a bit to get them used to this but if they tolerate a harness, that is the best option.
Going outside together without a leash is an option, but that really depends on their personality and will always carry a residual risk. If a cat gets startled by something, they are going to scale a 6 foot fence faster than you can blink.
Going outside once a week is likely going to introduce a new problem, they will enjoy the exploration and yearn to be outside more than you can offer.
This might entice them to find ways to escape the house, some of which may prove fatal on the first attempt, e.g. a tilted window where they can get stuck easily.
Looking at the topdown view of your property, I would suggest building them a catio as an ideal solution for all parties involved.
This can be as simple as a smallish cage they can reach from a ground floor window, even a balcony style cage where they can sit outside the window and have a better view is a start here.
Our cats have a huge outdoor enclosure, but we started with just a smallish cage as well and this already is a huge bit of participation in outside life for indoor-only cats.
Depending on your fence, it could be cat-proofed with little problems and investment, and you would have a very nice large outdoor enclosure.
If that is not an option, adding some additional fencing connecting to your main fence and cat-proofing just this might work, e.g. connecting top right and bottom right corners of the house to your main fence, effectively turning your garden area into an enclosure.
