You certainly can!
Young nymphs are great fun to handle, they can do no harm to us but can be very quick and be easy to lose if you don’t keep a watchful eye on them. If your nymph does manage to evade you then you will most likely find them in a high place. They like to climb upwards so check your walls and curtains!
When disturbed, some mantis species will flip and roll about like a piece of debris in the wind. Anyone that’s had a dead leaf or an orchid mantis will know what that’s like to see!
The bigger mantis species, especially the females can be; shall we say...temperamental. They can be a bit guarded and you need to treat them with respect. Try to get your mantis to walk onto you so that they will perceive you as something to climb on. If you rush your hand towards them and try to cup them they may act defensively. This can lead to your mantis grabbing you with their tibial spines and begin biting you. If this happens... TRY VERY HARD (easier said than done) not to flick around as this will hurt your mantis. Instead try to pry them off you using a pen or tongs. Your mantids instincts’ are to grab, hold on with all their strength and start eating. In the 15 years I’ve been keeping mantis this has never happened to me but I have had them grab each other through matings and the same procedure with tongs applies. Have tubs and tongs on hand just in case. I have been stabbed by tibial spines when handling geriatric females who have gripped my hands to steady themselves. Those spines do pierce the skin and boy do you feel it. For something so small they really do have a lot of power in them.
Whenever you do handle your mantis please do so carefully and over a surface or on the floor. Some mantis can be skittish, jumpy or try to fly and can be injured from a fall, especially fully grown adult females who are rather heavy bodied.
Note: Adult male mantis aren’t the best fliers in the insect kingdom but they can take off and flutter surprising distances. If you get your adult male mantis out to play you should double check your windows are shut beforehand and cover any gaps you don't want him to venture behind.
Important note: Before you handle your mantis always double check they aren’t about to go into moult or have just moulted. A mantis getting ready to moult will have gone off its food a day prior and its activity would have lessened. Strictly do not disturb them at this time. Please remove all food items as soon as you can.
A freshly moulted mantis will sometimes be paler than before, they might be slightly see-through and will be a bit floppy as well as a present exoskeleton discarded on the floor or hanging from a perch. Leave well alone in this case as they need time to harden before handling and feeding. I’d suggest leave alone for a good 24 hours for a small nymph, to a couple of days for an adult to be on the safe side.