I also have a 99 310 with rudder...

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I also have a 99 310 with rudder shaft seals leaking is it something that can break and cause serious problem / sinking 

How big of job what should I expect for cost

[wingless]

Welcome to the forum.

There is multiple layers of packing within the cap that seals the steering shaft, as shown in this image.

https://live.staticflickr.com/65535/49447435676_4230445927_c.jpg

The first step is to loosen the jam nut then slightly tighten the cap, to determine if the existing packing has sufficient lifetime remaining to stop the leak.

When I perform that adjustment I then operate the boat to determine if the adjustment is correct. I then snug the jam nut against the cap, to retain the setting.

If the packing has exceeded the lifetime then removal of old, replacement with new is required. The packing on my 2000 380DA was three layers of ¼" square wrapped around the shaft, w/ the ends cut at 45° and the ends at staggered rotation.

The "easy replacement is: when on the hard, put a floor jack under the rudder, pushing it hard up into the hull and remove all the steering stuff, scoop all the old packing out of the cap and replace w/ new.

On my boat access is fine. My guess is that access o the OP's 310DA is going to be the biggest issue.

[wingless]

Assuming the issue is typical dripping / not fully dry, then other then staining the bronze and wet in the bilge, not going to sink the boat.

If the cap has loosened / barely attached / large water ingress, then it is never good to require bilge pumps to remain ahead of the leak. If that's the case, yank the boat and fix.

If hiring for repair, the biggest costs are going to be yanking the boat and labor with cost depending on access.