I'm sure there are plenty of users here who might disagree with my approach, and some even recommending that you employ an auto-reversing tapping head with a clutch, but here is how I approach maching tapping on with the 935 and a jog (quick-acting forward/reverse) control over the spindle.
In smaller diameters, spiral flute taps are the most susceptible to breaking because of the smaller cross-section of the tap (relative to a straight flute, gun tap, spiral point, or whatever). A spiral point tap of the same size/pitch will have a larger cross section and thus less susceptible to breakage. Consequently, when I have a choice between the two - which usually relates to whether the hole being tapped it open or closed at the bottom - I will choose a spiral point tap that pushes the cut material forward and out the bottom. I bring this up simply because you can apply more torque to a spiral point tap than a spiral flute tap of the same size/pitch.
I routinely tap at 1/4-20 using a keyed drill chuck and a spiral point tap into an open hole using the jog function on my 935 in backgear. A keyless chuck may or may not have enough gripping power to tap 18mm deep with that tap into something like 1018 steel, and the chuck will likely loosen when the spindle is reversed, which is why I use a keyed chuck. At 1/4", a spiral flute tap into softer steel should be fine in a keyed chuck that is cinched down enough that it doesn't slip - down to 15mm for sure and perhaps to 20mm. This is where your choice of tapping fluid is important and needs to be matched to the material. In my experience, the tapping fluid type matters more with smaller diameters and needs to be matched to the material being tapped. Stainless steel is particularly problematic in that it work hardens easily if you start plunging down, then out, then down again, etc.
Obviously, the risk with a keyed chuck is that you have little control over the torque being applied to the tap, and risk the tap breaking. Does putting the tap in an ER16/25/32 collet help? Only to the degree you can tighten the collet nut to a precise enough value that the tap will spin before it breaks. I've fussed and fussed with this and given up. It's a path to frustration.
A tapping head will give you hand-pressure control over the applied torque which can be helpful but isn't a panacea. I have owned and used three different tapping heads. They give you more control over the torque applied to the tap, lessening the possibility of the tap breaking, and of course they auto-reverse when the quill pressure is released, which is convenient. But you have jog control over your spindle, so the auto-reverse of the tapping head is of marginal value. But tapping heads also eat up a tremendous amount of Z-height, and really limit what you can tackle with a 935 since there is no riser-block available for that machine.
I sold all three of my tapping heads and focus instead on using a keyed chuck (Vertex) while optimizing the type and brand of tap and tapping fluid selection. I use TapMagic formulated for aluminum, A9, or WD40 on non-ferrous materials, Anchor Lube on carbon steels, and Tap Magic 10004E EP-Xtra Cutting Fluid on stainless. I have also had good results with Moly Dee tapping fluid in stainless. I also go out of my way to buy taps that are high quality, preferring brands such as Widia (from McMaster), Hertel, OSG, Guhring (from MSCDirect), and Morse (from MariTool).
Hope this helps.