* Unit could fetch around 7 bln Swiss francs - analysts
* Move comes days after sale of Gerber Life Insurance
* Company says sticking with health science unit
* Hedge fund Third Point demanding bolder corporate moves (Changes headline, adds context, comments)
By Martinne Geller and John Revill
LONDON/ZURICH, Sept 20 (Reuters) - Nestle put its skin health unit up for sale on Thursday, as the maker of Nescafe and Perrier water ditches underperforming businesses and fends off criticism from an activist investor demanding an overhaul.
Nestle said it was exploring strategic options for the unit, saying "the future growth opportunities of Nestle Skin Health lie increasingly outside the group's strategic scope" and did not fit in with a sharper focus on food, drinks and nutritional health.
Nestle agreed this week to sell its Gerber Life Insurance business for $1.55 billion, while sources told Reuters it was also bidding for GlaxoSmithKline's Horlicks drink.
The skin health unit makes Cetaphil and Proactiv skin care brands, Restylane wrinkle fillers and prescription dermatology treatments. It had sales of 2.7 billion Swiss francs ($2.8 billion) last year, accounting for about 3 percent of Nestle's total.
Vontobel analyst Jean-Philippe Bertschy estimated the business was worth 6 billion to 6.5 billion francs, excluding financial debt, provisions and deferred taxes. He said it could fetch between 6 billion and 8 billion francs in a sale. Another analyst put the sale value at about 7 billion francs.
Nestle Skin Health was formed in 2014 when Nestle bought L'Oreal's stake in their Galderma dermatology venture.
Jefferies analyst Martin Deboo said the most likely exit options were a leveraged buyout or a sale to L'Oreal, if the French cosmetics firm followed Nestle in making a strategic U-turn.
L'Oreal, in which Nestle is a shareholder, declined to comment.
Nestle, the world's largest packaged food company, is under pressure from Third Point, a hedge fund run by investor Daniel Loeb, to take bold moves to improve returns.
Chief Executive Mark Schneider, the first externally hired CEO in nearly a century, has addressed several of Third Point's demands, including setting a margin target and speeding up acquisitions and divestitures.
The one demand he has not addressed is the sale of Nestle's 23 percent stake in L'Oreal, worth nearly 26 billion euros.
Baader Helvea analyst Andreas von Arx said the plan to exit skin health could reignite talk about the stake since that also lay outside the vision Nestle outlined on Thursday.
"Sharpening our strategic focus on Nestle's core food, beverage and nutritional health products offers the best opportunity for long-term profitable growth and is fully in line with the pursuit of our company's purpose," said Paul Bulcke, Nestle's chairman and former CEO.
When Bulcke ran Nestle, skin treatments were a major part of a push into higher growth and more profitable health products taken to counter a slowdown in its traditional food businesses.
But the unit has performed poorly, incurring one-off costs including inventory writedowns and a significant goodwill impairment this year. Last year, Nestle started restructuring the business, cutting jobs and closing a factory.
Divesting the business represents a symbolic break with the decisions of Schneider's predecessors, Jefferies' Deboo said.
"This in turn suggests that Schneider is being given full latitude to act in the interests of shareholder value, unbounded by the decisions of the past," he said.
Exiting skin health is something many analysts and investors had asked for, Baader Helvea's von Arx said, adding that it put Nestle "fully on track" to deliver on Schneider's promise last September to swap out as much as 10 percent of its portfolio.
Nestle has also sold its U.S. confectionery unit, and has done several deals in coffee, involving Starbucks and Blue Bottle.
The skin health review is due to be completed by mid-2019.
At the same time, Nestle said it remained committed to its health science unit, which sells medical nutritional products and bulked up with the purchase of a vitamin business this year.
Nestle shares were up nearly 1 percent at 1049 GMT.
$1 = 0.9668 Swiss francs Additional reporting by Sarah White in Paris; Editing by Sherry Jacob-Phillips and Edmund Blair