Washing a hen and eggs without shells

Just wondered if I should add any pet shampoo (currently used for dog and rabbits) to the warm water when I wash one of my hens?  She has rather a dirty bottom and I think it is time to give her a gentle wash.  I haven't washed any of my girls before as they haven't needed it.

Also she has been laying eggs without shells for a couple of weeks - these are her first eggs and I suspect that she may not be able to make shells or hasn't got the hang of it yet? (there is plenty of grit and oyster shell in the run).  Every couple of days I have been finding egg yolk under the perches and nesting area in the coop with the remains of what looks like the membrane inside a shell but no actual shell.  She did have some yolk on her bottom yesterday (which is why I think I need to give her a wash ).  I am keeping an eye on her to see if it is egg peritonitis (thanks to the info in other threads) but she seems perfectly well and her vent seems fine.  Any thoughts whether she will lay normal eggs?

Thanks Sassy. I seem to spend a lot of time these days washing my dog, rabbits and now chickens together with giving them all pedicures!  The Husband is at the end of the queue to have his hair clippered!! 

Chickens are all busy picking away at the moss in what is left of my lawn so I think she is just having problems getting into the swing of laying but will keep an eye on her...

Grinling - I've had the new girls since September last year (quarantined for at least 6 weeks), bought from a specialist established breeder, did not see specific henhouse but saw general set up, no runny eyes or diarrhoea on any of them (old or new).  Not see any signs of mycoplasmia and they all seems in good health. 

I think dirty bottom is more due to sitting on poop which sticks to the feathers (they like to poop in the nesting area on the coop despite my efforts  ) and the new girls are white so it really shows.  I do need to worm them soon so that may help but will keep a beady eye on them all the same...