This is a very easy problem to solve. However Oliveros, there is not enough information in your original statement.
I will go with the assumptions presented to date and assume a rotary seal. Please note there are other seal types, static, dynamic (reciprocating, pneumatic floating and rotary) as well as face seal alternatives. Each of these introduces the variance of elastomer compression, that is, squeeze. The squeeze also depends on the diameter of the o-ring specified. Commercial available types are 0.070, 0.103, 0.139, 0.210 and 0.275 diameters which coincide to 000, 100, 200, 300 and 400 series o-rings respectively.
For the shaft size specified, 1.0 cm or 0.394 inches, I would use a 000-045 Series o-ring because machining the male o-ring groove would weaken the shaft somewhat. It is more cost effective to machine a male groove rather than female because the machinist has much more control on the external profile. In the elastomer series selected for rotary application, the squeeze is no greater than 11% for 200-1500 RPMs. Thus the gland specifications are 0.262/0.260 diameter X 0.075/0.079 inch wide; this gives a mid range squeeze, approximately 5.5%. Your mating piece must therefore be drilled and reamed 0.396/0.398 diamter with 63 Ra finish. A number 2-010 o-ring (0.239 ID X 0.070 CS diameter) should be used.
Now check the elastomer stretch, typically 2% to 3%. I get 9.6% which is really, really high for the application. Expect o-ring necking to lessen your squeeze, but you are in no-mans land since the a 2-011 o-ring is too large for the groove specified. A quick review for a female groove cut into the cylinder of the mating piece gives no additional advantages. Similarly, going to a 100 Series o-ring would only weaken the shaft in male groove design or present manufacturing issues with female groove design.
Finally look to lessen elastomer stretch by lessing the sqeeze. You're talking 30m of seawater, I would argue not much pressure and the o-ring selected is good for 1500 psi without the necessity to resort to backup rings. Going to a 2% squeeze would imply a male groove specification of 0.259/0.257 dia X 0.075/0.079 inch wide, the stretch drops to 8.4%. This is still on the high side, but professionally speaking, I've used specified worse with experiencing problems. For the sake of discussion go with it using 2-010 o-ring.
Now select material, dependent on fluid application and temperature only. Nitrile is acceptable, I'm a big fan of a flurocarbon alternative like Viton. The typical durometer or rubber hardness is 70.
In summary, cut a 0.259/0.257 diamter male groove, 0.075/0.79 inches long into the shaft and give 0.02R fillets in the groove, 0.005/0.007R shoulder fillets. The surface finish is 63 Ra. Drill and ream the cylinder or mating piece to the shaft, 0.396/0.398 inch diamter with interior finish 63 Ra. Specifiy a 2-010 o-ring, Parker-Hannifin Corporation made of Viton, durometer 70.
...and there you have it...
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada