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Well if you’re going to force me to go on your adventure without an immersion suit and leave it up to a novice, this is what i will do.

The problem as I see it is how much weight are you willing to carry for safety on the ice, versus whatever else you are out there for in the first place. How much room on and in a pack will you dedicate to safety. There are lots of things you could bring to ensure survival and rig a bag just for that purpose.

This is what I want for your scenario assuming this is a backpacking trip away from help.
1 set of Ice Claws
A light weight bag with a single shoulder strap cross body carry. The bag has to have large nylon zipper, lubed with “zipper eaze” and large pulls with additional small straps on the pulls.
Inside the shoulder bag in a vacuum packed bag:
Stored in ziplock freezer bags
Mid weight polypropylene long underwear top & bottom or union suit, socks, mittens, fleece hat
Thinsulate Boot Liners
2 tall kitchen trash bags to be used as boots over liners
Light weight wind breaker Jacket & Pants, Velco front closure, elastic waist pants.
Emergency Survival Sleep Space Blanket Bag.
10 Large exothermic hand warmers
Butane lighter, strike anywhere matches, ferro rod & striker
5″x 7″ file card
Small baggie of magnesium shavings
5 oz of thermite
1 drum liner trash bag to stand on and later for all my wet clothes.

If I have a backpack I want a positive flotation pool noodle strapped to the bag in a u across the bottom and sides.
On the left shoulder strap 50 ft of para-cord folded for throwing, attached to a 3″ Oval Shaped Plastic Rope Float. Light Velcro straps holding the bundle.
Everything in the backpack has to be in water proof bags.

If you go in; throw the weighted cord as far as possible toward the way in.
One attempt out with back pack on
Dump pack if ice breaks
Climb out and slide away from the hole toward the way in
Remove safety bag
Open safety bag and zip locks with clothing, do not remove contents
Open hand warmer bag. rip open hand warmers using ice claws if necessary
Put on hat
Remove wet top layers and put on dry tops and wind breaker
Remove bottom layers, socks boots
Put on dry bottoms, socks boot liners, bags on feet and wind pants
Place hand warmers in long underwear top and bottom, and pockets for hands.
Close safety bag and re-sling
Stuff wet clothes in large trash bag
Pull Backpack from water
Drag clothes and back pack to shore if possible, but clothing must make it to shore
Find a dead tree down fall, dead branches plastic bottles a boat or anything that will burn and as much of it as you can fast.
Put the the bag of magnesium in the thermite bag and put both in the fire pile. Light the magnesium with a strip of the card and move away from the thermite. Make the fire as large as possible without starting a forest fire.
Put on your space blanket sleeping bag and use the hand warmers next to the fire and hope you live. If you manage to live, keep the fire going and dry your wet clothing by the fire. When it’s all dry you can either walk out and go home or go get your frozen backpack off the ice. Hope your cars keys are in your pocket.

Edit: At this point your so paranoid about falling in through the ice you pre-stage a bonfire in a sheltered spot on shore before you venture across, including a leanto and a thick bed of dry leaves.