What tree diseases are you hearing about? I doubt that any would affect vegetables, though if you're putting the mulch near a tree, it might be of some concern. White and black walnut trees contain juglone, which can be used as a herbicide, which is growth-stunting. Other than that, I'd say you're good to go.

To the extent that you eventually want it to compost in situ, thinner cuts are better. To the extent you want it to hang around as a semi-permanent top mulch, I guess the chips and bark are better.

Around here we have oak wilt, which kills many oak trees. Mulch from the wood of those trees would NEVER be offered to anyone, and I think those infected trees are incinerated.

I wouldn't worry about tree diseases but adding a lot of uncomposted wood fines could lead to soil health issues if you work it into soil at a future date. Usually it is fine if left on top of the soil surface especially for acid loving plants. For vegetables you are better to use a less dense mulch that is more readily decomposed. If you use it I would suggest that you either limit it to an inch or less if you will incorporate, If you rake the bulk off then you probably could apply more. At any rate you should probably apply extra nitrogen and be sure to monitor pH for next spring.

Adding uncomposted shredded wood to a soil bed is fine, as long as you don't add a lot at one time, and as long as it can compost in situ in the soil before you start serious growing in it. I dig browns into the soil at the end of the growing season, turn it all over once or twice and, three or four months later, it is entirely integrated into the soil food web. To the extent the brown stuff stays on top during the growing season, there is really nothing to worry about. I pile on dried shredded leaves early in the growing season, mainly to keep moisture in.