I fly all over with tools, camera gear, electronic equipment, and a metal detector.   I throw all the tools into a couple pelican (or Harbor Freight) cases, making sure everything is snug.  I pad it with clothes and socks to wear later.    No one has ever given me trouble for anything except for my XP Deus metal detector - they HATE  it at customs.  Everything goes into checked baggage.

Another option is to ship your tools ahead via a major parcel carrier. Or just ship the tools that may make you look suspicious.

This is where having a second set of tools you don't care about comes in handy. Leave the fancy soldering iron at home and bring (or ship) that old 25w Radio Shack iron that's in the back of your closet.

Can your school or work give you a note stating why you need those items so that can show it to the security personnel at the airport when you do get stopped for questioning and search?

If so, make a few extra copies so that security and similar officials can have one to keep.  

So long and tell, Trillian, "Hello" for me.

I used to travel with tools a lot, and one thing that was helpful was to have business cards with me listing a technical occupation. Several times the security people asked for some proof that it was a legitimate business trip, and the cards were sufficient. In the US, flying has become such a hassle, that I generally drive instead. Not useful for trans-oceanic obviously.

I had a pair of crimpers confiscated.  

It seems to be hit or miss with them.  Other than batteries, I try to stow everything down below.

I had my soldering iron confiscated once by airport security, because it had a trigger.

https://www.google.com/search?q=lutola+75&rlz=1CDGOYI_enUS931US931&hl=en-US&prmd=sivxn&sxsrf=AOaemvK108W9Lxl3uvnFZYi8frpuF39_UA:1629940123844&source=lnms&tbm=isch&sa=X&ved=2ahUKEwiUndaQwM3yAhVnJTQIHYpiB44Q_AUoAnoECAIQAg&biw=414&bih=720&dpr=2

Lutola?  I'd stop you for antiques smuggling :)

Haha, that's fair. I had Lutola clone, made by ZDZ. They still make them though.

Having said that, I moved to Weller a few years ago and I’m not looking back :).

While I was doing college classes a couple of years ago I had to do some traveling and had to take my Oscope, multimeter, power supply ect. I made sure to pack them will with some spare pick and pluck foam I had laying around. Everything showed up undamaged and functioned properly when I tested it out. I would always recommend checking that bag. My bag was searched they left a note as they should, just make sure that it is organized and you know what you packed just in case something goes missing that way you can attempt to claim it if you so choose. Fly safe and happy hacking.

Some of these items, such as your multimeter, may be built to handle the trip through checked baggage nicely. Others, like your power supply, could be delicate enough to warrant a space in carry-on luggage. Some of this will largely come down to managing how precious they are to you, their actual intrinsic value, and your baggage allowance(s). One note of advice for carry-on pieces is to ensure that they can be unpacked and repacked reasonably easily should you indeed have to take a look through the bag with security. Having a carry-on bag that facilitates this is helpful (so a deep duffel or narrow-throated backpack is NOT necessarily the best choice unless you're a pro - especially considering that security will usually not want you handling the unpacking step). Do also take into consideration what your gear looks like when stowed in your carry-on. I accidentally  grabbed a work bag for a quick trip which had some RF filters in a pocket. These thick, cylindrical metal filters sat at the bottom of the bag all screwed together for convenience... so I'd say I totally deserved getting pulled aside for that peek by security!

Note that some "regular" tools are indeed restricted to checked-bags, so check your Canadian transportation authority there as those rules can vary (for those in the U.S., for example, knitting needles get a pass but large screwdrivers are out: https://www.tsa.gov/travel/security-screening/whatcanibring/household-and-tools ).

Good luck!