I’ve used this type (mushroom plugs - as shown above) twice now. Very effective, and can be installed without taking the wheel off the car, but only just.
On both occasions the rear tyres picked up the punctures, and on both occasions the hardest part was getting the offending penetrant out of the tyre. The first was a wood screw, which refused to budge with pliers so I borrowed a screwdriver to unscrew it. The second puncture was a piece of metal that I think used to be a clip for holding on a wheel balancing weight (oh the irony). That took twenty minutes to remove with a pair of pliers, mainly due to the very restricted amount of space in which to work when the wheel is still on the car.
Once the items are removed plugging the holes takes seconds. They hold air reasonably well too.
The only downside to these plugs is that they will only accommodate a certain size of hole. The alternative kits with part cured rubber strings can be used to plug up enormous holes and tears to get you out of a bind that the mushrooms cannot.
If you’ve fitted mudguards, beware. With a flat tyre on 20”rims the amount of room to work in is tiny. On 18”s the car will be sat an inch lower down on a flat tyre, so keep a tool in the car to remove the mud flap as well.