Hi and welcome.
Yes that is very doable. I have walked those in a day with my son. Just a few years back.
We stayed at Burnthwait Farm in Wasdale Head. The route we choose was to start up Ligmell Beck to Great end, which we scrambled up via Cust Gully, it was more of a water fall than a gully on the day. From Great End we made our way through the fog to Ill Grag then across the clitter to Broad Crag. Then on to the path and up to the Cairn at Scafell Pike. Next it was down to Mickledore , around the base of BroadStand, ( too wet for us to consider on the day) and up to the mid point of Lords Rake, where we branched left into the heart of the mountain and followed the track that comes out at Symonds Knot. Then an easy walk to Scafell, where we finally got a view, as the clouds briefly parted for us. We took the full Lords Rake route back down and finally followed the tourist steps/path back to the pub.
Even on a pretty poor day we enjoyed it immensely. It's not a straight forward route, there is scree and scrambling involved, but nothing too difficult in decent weather. On a wet day though I would not attempt Cust Gully without a rope. I gather it is easy enough to go around, but I have not done that bit.
Hope you get the Opportunity to do it.
Plenty of more local folk here to offer you further advice so I will sign off for now.
EDIT:- A plot of our route can be found here.
https://osmaps.ordnancesurvey.co.uk/route/2482213/Scafell-with-EddAnd after a little searching I found a trip report for that walk, on a car forum I frequent far too much. Ignore the car bits unless like me you love driving too.
https://z4-forum.com/forum/viewtopic.php?f=14&t=109200&p=1579830&hilit=gully#p1579830Enjoy.