I used to sell Seco - I wouldn't hesitate for a moment to recommend an SD522 drill for drilling short diameters, with flood coolant. Keep in mind, that the coolant's main fuction is to flush chips from the flutes - especially at deeper depths - while drilling. With short drilling depths, the chips will come out on their own without much issue.
IF chip evacuation becomes an issue, a macro with a short dwell - not a peck - to break the chips would help. I doubt there would be a need for this however.
On the 1.187 +/- .005" holes - My only concern would be holding that tolerance. Especially without the thru-coolant. I would expect poorer hole quality, as there will be more opportunity for scarring/galling/scratching of the hole from the dry/un-lubricated chips.
There are coolant-inducing tool-holders on the market, to induce coolant to the tool, for older machines. These add cost of course, but more importantly they add gage-length, which is going to be a big No-No for this style drill, on a 40-taper machine. So that's not really going to be an option.
Since you're going to be using an endmill to counterbore these anyway, my suggestion would be to use a 1.125" indexable drill, and then finish with an endmill. If you insist that the extra cycle-time will hurt, then buy the 1.187 drill on a guaranteed-performance basis. That way, if the drill won't hold size, you should be able to return the drill.
Also - Use a SHORT series weldon holder to hold the drill - This will offer 1" shorter gage-length, which will be very valuable on your 40-taper machine.
(Edit: Actually, 2"... See below...)
1.125 Drill -
SD522-1125-225-1250R7 | Secotools.com
1.187 Drill -
SD522-1187-237-1250R7 | Secotools.com
Inner Inserts -
SPGX0903-C1 T400D | Secotools.com
Outer Inserts, 1st choice -
SCGX09T308-P1 DP3000 | Secotools.com
Outer Inserts, 2nd choice* -
SCGX09T308-P1 T250D | Secotools.com
*This insert uses a PVD coating. It will not have the same wear resistance, but will offer a 'sharper' cutting edge, and may be necessary if you see built-up-edge problems with your gummy Stainless material, and no thru-coolant.
Short/Stubby Weldon Holder* -
CAT40 1.1/4 End Mill Holder Stub Length
*You may have to cut the shank of the drill slightly to get the flange to bottom out on the face of the holder, but I would 100% do it. This holder will save you 2" of gage-length over a 'standard' length holder..."
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Regarding your .662/.665 thru hole, indexable-insert drills are near worthless at this small diameter. Even replaceable-tip drills like Iscar's Cham-Drill are tough at these smaller diameters, when solid-carbide drills have come so far in terms of cost, and performance.
Here's a quick recommendation, although I'm not up to speed on Carbide Drills as I once was. Walter DC160. It may be worth a call to Walter for a better recommendation, as the DC160
may be a double-margin drill, which would be a No-No for drilling soft stainless with flood coolant.
Walter DC160 16.8mm Drill -
https://gps.walter-tools.com/toucht...oQaDkn9I0hUvrA==#/trs/productInfo/productData
Another solid contender for drilling Stainless, is
Mitsubishi's MVS lineup.
http://www.mitsubishicarbide.net/mmus/enus/drilling/20000192/20092269
Best of luck.