you actually only need to wait something like 5 + X days.
you need 172 days to count for a full year and the HBD season is 176 days long. so technically, 5 days in the minors is enough, but if a player is called up after spending <20 games in the minors, they get transferred to his ML total. since 20 is the minimum "chunk" of time that can be spent in the minors, that's the magic # for delaying arb.
so if you have him on your team for the last 75 days, you only need to wait an extra 60 (if i have the numbers straight) next year to not tick towards arb. but that's a bit of a pain, so i would just call him up and leave him up.