Yes, to an Extent
Yes, there are non-combat manoeuvre options and techniques, though they're spread thinner than combat ones. The line between the two can be blurrier than usual, as GURPS deliberately rejects application of combat-like structure to many other areas (most notably social interactions). In practice, there's usually just the situation in which additional details and a skill modifier apply, and if it's a penalty, it can also be bought off as a Technique (or, in other cases, negated or reduced by a Perk); there's no formal tagging as a 'noncombat option' or 'manoeuvre option'.
Social Techniques are probably the most numerous of the noncombat ones, though even they aren't as numerous as combat ones.
Example of a Social Techniques
A favourite example of a social technique is Elicitation. Normally, one can either just use Carousing at +0 in a request for information, trying to use the atmosphere of an enjoyable courtly ball or punky rave (whichever is appropriate for the setting, situation, and the character's Familiarities) to ask people to share rumours about the local leader.
But that has the downside of people realising what kind of data one is trying to dig up. If you want to avoid that, you can try a harder, subtler approach, known as Elicitation:
In fact, ideally, the subject doesn’t realize he was being questioned, or doesn’t know what the topic was! [ . . . ] The questioner approaches the topic indirectly, while overtly seeming to converse about something else; apply a penalty of the questioner’s choice to the Influence skill, and the same penalty to the subject’s Will.
The above is a partial excerpt from Social Engineering, just to demonstrate what such Techniques tend to be like.
Where to Find Them
GURPS Social Engineering is a major source of extra detail on game-mechanical handling of all sorts of social stuff - persuading people, cultivating a media persona, manoeuvring through bureaucratic and/or political landscapes etc. The accompanying release of Pyramid (54) expands on it, lists more Techniques, and adds social Styles.
GURPS Low-Tech Contains a handful of Techniques related to medicine and riding.
GURPS Thaumatology: Chinese Elemental Powers and GURPS Psionic Powers have rules that employ Techniques and modifiers applied to supernatural abilities, though those are a mix of combat and noncombat ones.
The rest are rather few and far between, but hopefully the existing examples can serve as a basis on which you and the GM can build your own, once you're acquainted with the principles.