First, see if the new clutch cover plate fits without hitting the clutch studs, if no hit, then you are OK, no need to cut anything, if hit, them just use a Dremel tool to cut the studs, no need to disassemble the clutch.
It is better if you leave the clutch assembled when cutting the studs, that way you don't cut the studs too short, they need to protrude a wee dab above the clutch disk.
The small gear is on a taper, so it will probably be very difficult or impossible to remove without damage, so get the puller tool, you will be glad that you did, it will come in handy pulling the gears if you ever want to disassemble the engine for maintenance or cleaning.
If you don't have a Dremel, get that as well, it is a very, very useful tool to have, if there is a Harbor Freight Tools store near you, they have this one it's on sale now:
Professional 4 Speed Rotary Tool Kit
Use a 20% off coupon and the price gets knocked down to $11.98!
Let me know how it goes.