What were an American soldier's chances of being wounded on the front lines of Vietnam?

I'm not sure the exact info you are asking for, but the National Archives have a site with some various statistics. The simplest which may answer your question would be the Hostile/Non-Hostile death numbers:

HOSTILE DEATH        47,434

NON HOSTILE DEATH    10,786

Total Records

58,220

As you question states, the helicopter really changed the definition of front-line, so this may at least break down the difference between combat deaths and others. Some other tables on the site also show a further classification of casualties:

Casualty Category                  Number of Records
ACCIDENT                                   9,107
DECLARED DEAD                              1,201
DIED OF WOUNDS                             5,299
HOMICIDE                                     236
ILLNESS                                      938
KILLED IN ACTION                          40,934
PRESUMED DEAD (BODY REMAINS RECOVERED)        32
PRESUMED DEAD (BODY REMAINS NOT RECOVERED)    91
SELF-INFLICTED                               382

Total Records

58,220

Seeing your last comment, I don't see any other tables at this site which might provide a 'front-line' vs 'rear area' type breakdown. There is a table concerning injuries by paygrade but it holds no great surprises.

In all wars the risk very much depends what unit you end up in. Consider the British Army XXX Corps: El Alamein, Tunisia, Sicily, Normandy, Market Garden, Ardennes, Rhineland. So to speak of risk as if it is even across an army is deeply misleading.

The Pacific War was, as it's name suggests, dominated by the ocean and thus sea and air power. The ground forces were engaged in short vicious battles for small islands. It's not surprising that the absolute number of days in combat were low. Conversely, the number of days in theatre were high: in a ship in the middle of the Pacific you can't take a weekend's leave. The Pacific War is an outlier and comparisons are not really informative.

You mention helicopters for delivering soldiers to battle without also considering that they rapidly extract the wounded from battle. Prompt and excellent medical treatment for US troops lead to fewer deaths than previous conflicts (eg, compare with the Casualty Clearing Stations of WWI). The corollary of that improvement is a higher proportion of wounded.

How do you classify "soldiers serving as front-line troops"? Consider that guarding the US Embassy in Saigon was a soft posting. Right up to the day of the Tet Offensive, upon which it was the "front line".

Finally, there was a emphasis on wounding US troops, and the statistics show that this emphasis had effect. Around 30% of all wounds in Vietnam were due to low technology improvised weapons: pits and traps with bamboo stakes, repurposed grenades and bullets, car bombs outside hotels. This was low risk warfare on the cheap, but still effective at removing experienced troops from the field.

At the risk of not answering the question directly, I think it's more interesting to put the stat in context than it is to try to figure out the precise number.

In the event you haven't seen it already, I can only recommend spending a few hours watching Ken Burn's The Vietnam War. The most vivid recollection I have from it, besides the political scheming, was how the US troops were constantly instructed to capture hills throughout the conflict. They'd come out victorious, of course, but would then be instructed to abandon their position days or weeks later instead of holding the hill - with the enemy settling back in shortly after.

That is, I would surmise, the reason the casualty rate was so high: in addition to the day to day ambushes and soldiers never really knowing who they can trust in the civilian population, in open battle the US was often fighting uphill battles - which is the exemplar unfavorable battle position.

With respect to the casualty statistic proper, Vietnam War Statistics (Wayback machine) holds that:

• Between 1 - 1.6 million (40 - 60%) either fought in combat, provided close support or were at least fairly regularly exposed to enemy attack.
• 58,202 were killed
• 303,704 were wounded, of which:
• 150,375 required no hospital care
• 153,329 required hospital care, of which:
• 75,000 were severely disabled (lost limbs, complete disablement)

So you're looking at somewhere between 22% and 36% of soldiers who were exposed to fighting would have been wounded in some way; about half of those required hospital treatment, and about half of those were severely disabled.

(It's likely more interesting a stat than infantry vs support, since infantry can also mean guard duty at some safe place, whereas support can occur under artillery fire.)