I have a guide looking to build an Alaskan hunting rifle and he likes an old 1908 Sparkbrook SMLE #1 and wishes to rebarrel it to 405 Win.

I am sure it can be done, but my question is whether or not it is safe ?

Safe? Do some math and calculate the back thrust. Use the internal diameter, not the OD; that is misleading. It is not the chamber pressure that is important.
Compare that with a 303. I have done it but have forgot the results.
I make them into 405 2.2 inch; and use the more available 30-40 brass. 405 Teddy I call it.

I just answered this same question on the NE Forum, check it out!

Roger

Need to more fully flesh out all the ramifications in doing so.
It is not chamber pressure that is important; as I said. Calculate back thrust for each and you will get a better idea of what is happening.
The standard 405 will fit 3 rounds into a #3 Magazine (I just did it) before the angle gets too steep; it is about .030 too long, factory length. It would be very easy to seat a little deeper, or file off the lead tip a bit, or trim off a bit of brass; then it will work.
I have the 45-90 article from Rifle mag if anyone wants a copy.
Also, a 45-70 diameter rim will not work in an Enfield; some conversions ream out the bolt head support; I do not like to do that so I make them using slightly reduced rim, brass. Still works in all other 45-70/90 rifles. I know, not your question.