I've purchased a second hand Mountain Buggy carrycot and I believe the previous owners had it in a space that they smoked in. Is it safe to wash and use or will there still be residue and risk of SIDS. Is it also ok to let a newborn sleep in this product? Thanks

There is not a great deal of current research in relation to “Third - hand smoke”  & SIDS, however, it is generally recommended to avoid exposing a baby to any environment whenever there is a residual smell of smoke.
The risk to baby in relation to smoking, is “dose related”  ie the greater the exposure, the greater the risk.

Red Nose recommends that the safest place for baby to sleep is in a cot that meets the Mandatory Australian Standards.
From what I can see from on-line images of the Mountain Buggy carrycot, it appears to be more like a pram/bassinet type product.
The following are the recommendations for sleeping baby in a pram or bassinet.

Bassinets
There are no Mandatory Standards in Australia for bassinets.
Red Nose has the following general information about bassinets.

As there is no Australian Standard for bassinets, we are careful to keep up to date with reports of accidents associated with their use.
To date, the most frequent accidents associated with bassinet use are falls and suffocation hazards.
https://rednose.org.au/article/bassinettes

Risk of fall may be greater if the sides are soft or low.
Product Safety Australia has included some “Buying Tips” on their website, which may be helpful in determining the safety of any bassinet.

Ensure the sides of the bassinette are at least 300 mm higher than the top of the mattress base.
Ensure it has a wide stable base and a sturdy bottom so that it won’t tip over.
Ensure the mattress fits well and is firm, smooth and no more than 75 mm thick.
If the product has folding legs, make sure it cannot accidentally fold during use.
https://www.productsafety.gov.au/products/babies-kids/kids-furniture/bassinettes

Prams

Never leave your baby unattended in a pram or stroller. It is not a substitute for a cot.
https://rednose.org.au/article/prams-and-strollers

Avoid sleeping children in prams or strollers.
Never have an unharnessed child asleep in a pram or stroller as they can move about and may be at risk of falling or entrapment.
If they are asleep, maintain regular supervision.
https://www.productsafety.gov.au/products/babies-kids/kids-equipment/prams-strollers