Just to add some food for thought, the filter can provide quite a bit of sound muffling versus open air discharge. As such, if noise is your primary concern then you may wish to reconsider losing the filter. A lot of the noise is turbulence created at the impeller and with a straight discharge path to outdoors the noise will be loudest in whatever direction you aim the exhaust. You could build your own muffler for the DC, but it will likely cost you much of your gains in CFMs and SP that losing the filter would have gained you. If you do elect to remove the filter, do direct the discharge outside the shed as you do not want the fines accumulating in an enclosed space.
That said, removing the filter from the equation with a straight and uninterrupted path outdoors can gain you some extra CFMs and/or SP, if the noise is acceptable.
Just remember that a cyclone will only discharge the very finest (and most unhealthy) of dust particles, so if discharging open air then it is important to ensure that there are no windows for some distance to either side and no other sources of air intake (such as an HVAC air exchanger) within range of the discharge or you can severely pollute indoor air -- this includes any nearby neighbors if they happen to be nearby and downwind while it is running. It is also worth considering that the outdoor discharge will leave your shop negatively pressurized and that makeup air will have to come from someplace, possibly drawing back in the fine dust you have just discharged (particularly on days with little wind to disperse the fines). On the positive side, most of our shop tools do not produce a lot of fine dust if their cutting edges are kept sharp -- it is sanding that is the worst offender by far, so if you do not use the DC to capture sanding dust then your fine particle emissions will be much lower than if you do use the DC to capture those fines.
You will still want to be vigilant to avoid overflowing your waste bin since such would result in a buildup of flammable sawdust next to your house (if you do overflow, just cleanup any accumulation near the house).
If you condition your indoor shop air (heat, a/c, dehumidifier) then you will be exhausting that air and quickly, very quickly, replacing it with unconditioned air from outdoors, which may cause dramatic swings in humidity and temperature in an otherwise well conditioned shop. This is only a concern for conditioned shops as unconditioned shops will already be reasonably close to ambient conditions.
Regardless of what you decide to do with respect to discharge, I am very much a proponent of moving DCs and shop air compressors into an interior, sound dampened, closet or exterior shed if the opportunity permits as it eliminates a lot of noise from the shop and frees up some wall and floor space. Just don't let their remote location lull you into forgetting to perform regular maintenance (especially emptying the waste bin frequently). Unfortunately, my DC and compressors all reside in my shop as I don't have a suitable location to relocate them!
Just my $0.02.