Yes! I use 70% alcohol gel. DSD is immunocompromised so we bought a load to make sure we didn't bring Covid into the house. It is quite runny and does smell of alcohol, but is fab for removing glue.
I use Gorilla wood glue for the wooden pieces because it is very good at sticking wood together (who knew!) - it either is PVA or is very like PVA (the kind that peels off your fingers). I squeeze enough for the immediate job onto a sheet of paper and use cotton buds to spread the glue onto the pieces that need glueing then wipe the top with a tissue before closing - I've had the glue dispenser bit get too glued up to be any use otherwise. This is good for about 5-10 minutes before drying out.
I use an all-purpose warer-based glue for sticking anything else to wood or each other. This sets more quickly but can get messy. Do not use superglue because too much ends up on fingers... Again I squeeze it onto paper but use much less as it goes off in less than a minute. I use a pin or dip the item directly in the glue because cotton buds end up stuck to the paper or the glue or the desk.