If this is a minimum service temperature, I would not recommend using 416 stainless steel. At -46 deg C, the 416 stainless would not exhibit adequate toughness as a pump shaft material. For ambient temperature service, I would say yes.
416 shows high machinability but poor toughness even at room temperature perticullary if annealed/H+T and cold drawn. Despite this poor performance, a lot of bars are machined to produce pump shafts used for drinking water (not salt water , waste and so on ). I don't know the enviroment where your pump shaft will work but I think that a soft martenstic stainless steel ( as 1.4418 EN 10088 ) or a martensitic precipitation hardening as AISI 630 ( 1.4542 EN10088) in condition H1150 will guarantee highest KV at lowest temperature and high Rp0,2 and Rm.
Obviously, machinability will be strongly reduced but if you require an AISI 630 with S= 0,02-0,03% , this matter could be reduced. Soft Martensitic , as 1.4418 -very popoular in North Europe- is usually supplied with S= 0,010 -0,020%. About machinability, AISI 630 is better and cheaper (Molibdenum alloy surcharge). A lot of automotive industries machines this grade for high pressure common rail diesel system and has not problems. An other choise, it could be an Austenitic stainless steel as AISI 304 supplied in cold drawn bars in order to obtaine same mechanical properties ( Rp0,2, Rm )of 416 H+T. Kv at -45°C will be highest. In order to increase machinability, you can ask a Calcium Treated 304 grade. There is a lot of SteelMakers who produces austenitic grades by this methode,but -in my opinion- only 3 or 4 brands assures high reliability in terms of repetitivity of results about machinability.
I checked with the pump manufacturer. They told me that ASTM A582-Gr416 is their standard shaft material for -46 DegC. But I am still not comfortable with it.