Reddit mentions of Park Tool Razor A Kick Scooter (Clear/Black)

You are correct -- the only difference between the 11 speed KICKR and the 10 speed KICKR is the cassette. They even share the same freehub, which is the thing the cassette sits on.

You'll need to replace the 11 speed cassette with a 10 speed one. You will need some special tools to do this, though. Are you having your KICKR delivered to your LBS? If so, I'd have them do the swap. If not, you'll need this (or it's cheaper alternative here), one of [these] these, and a large adjustable wrench.

After you collect those things, here's a nice video showing you how to do the swap. Instructions are the same even for your KICKR.

If you haven't already purchased a new cassette, get the cheapest one. Weight is of no concern for indoor training -- no need to be a "weight weenie." If there's any guidance to be had with choosing a cassette for a KICKR, I'd stick with the same gearing (i.e., if your rear wheel is a 11-25, get an 11-25 for the KICKR. That way there won't be any adjustment issues between the KICKR and your rear wheel.

OP, to chain a cassette you'll need a chain whip and a cassette tool. Total cost for the two tools is about $30, but you can go cheaper if you buy off-brand tools instead of Park Tool.

Please note that the links provided are just quick-n-dirty suggestions. Some of the Park Tool sets would cover a lot of these things, but when building from frameset up... you may want to seek out a shop with the odd tools you might only use once or twice in your life.

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Aside from the standard tools, like box wrenches, cone wrenches, Allen wrenches (aka hex keys), flathead and Phillips head drivers, Grease... you'll need tools for:

• seating the fork race
  
• installing the bottom bracket (or press fit or one of a few other types?)
  
• cutting cable & cable housing
  
  In addition, you may need:
  
  
• adjustable crescent wrenches
  
• facing and chasing the BB threads
  
• at least a 5 nM torqe wrench, perhaps a 6 nM as well
  
• chainwhip tool
  
• spoke nipple wrench
  
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  I'm sure you could "get away" with less, or perhaps the Park Tool Advanced Kit but there's a reason for these tools. Good luck.

Tools. Most people don't have proper bike tools, so that would be a great surprise. You can either get a decent multi-tool (get one with a chain-breaker and tire wrenches) or a variety of Park Tools. Here are some Park Tools that I find invaluable: 3-way hex, chain cleaning tools, pedal wrench, and/or a chain whip

This bar tape is amazing 3mm Fizik performance. Tape should be replaced semi-regularly, but most people don't, so it would be a great surprise gift. Black looks good on almost every bike.

> just because I do not have the tools to remove the cassette on the rear wheel

This is so easy to do, and the tools are not that expensive. Pick up a Park FR-5 and a Park SR-1 for < $30 and you'll be able to take your cassette off whenever you need to.

The following will get you out of most mechanical issues:
workstand
mini ratchet
set of hex bits for ratchet
1-10ish Nm torque wrench
10-100ish Nm torque wrench with adapter for 1/4" drive bits
Park spoke keys
homemade bearing/bb press out of plumbing odds and ends
Park chain checker
Park mini chain tool
Park chain whip
Park master link pliers
Park hollowtech crank cap tool