For sure, a good soldering iron is a must, but needn't be super expensive. It should have temperature control, ESD (electrostatic discharge) safe, and various tips from small to medium (relatively). I see examples that look OK for $40-50USD, but can't confirm. Some Kester or Multicore electronics solder, 63/37 rosin core, small diameter. For reflow, you may want solder paste.
Hand tools:
Fine flush wire cutters and insulation strippers. Hakko CHP-170 flush cutters work well and only $5. I use Ideal wire strippers, red handle T-Stripper for small sizes, maybe $10.
Small needle nose pliers. Several tweezers for handling LEDs and MCPCBs. I like angled stainless, but also have teeny straight ones (Hakko 3-SA, $10).
Screwdrivers, like a jeweler's set. Anything from manufacturers like Wiha are worthwhile. The Wiha chip lifter tool is one of my favorites - as a prybar!
I reflow using an old travel iron (for clothes!) set upside down in a Panavise. Even has temperature control!
A soft-jaw vise and/or helping hands jig to hold things. I also use little pieces of rubber or neoprene pads in the jaws.
A modest DMM (digital multi meter) for checking voltages and testing LEDs. Best if the diode check mode can light up an LED, not all do AFAIK.
Depending on your eyes, consider some loupes or magnifiers; good lighting, a fan to blow soldering smoke away. I like plastic trays with sections to store disassembled parts and keep things from rolling away.
I use a heat gun to break down Loctite (it softens at something like 400F). However, this is problematic on many lights as there may be major parts inside made of soft plastic. Also, some lights use glues other than Loctite type. Note, if you reassemble lights, Loctite and clones don't set inside aluminum or anodized aluminum. You can get it to set using a special activator. Or use another glue.
Of course, you may need regular hand tools (screwdrivers, pliers, wrenches), a soft tubing vise jaws, rubber strap wrenches, depending on what you have to take apart.