Can I watch Daredevil (2003) and Punisher (2004) without spoiling the Netflix series?

There is little or NO connection between the early 2000's movies of Daredevil &/or Punisher to the latest TV incarnations.

They are completely stand alone.

They may bear some common characteristics but since they are based on the original comics this is not surprising.

Daredevil Seasons 1 / 2 on TV do not really cover the same ground as Daredevil "the Movie" (except an origin story) and the death of a supporting character in the TV series (S2) is also covered in the movie to a greater extent (but differently). Again, this is covered in the comics...so no surprise there.

Since we don't know what will happen in The Punisher TV series we can't comment... although I expect Frank Castle's origin story (if covered at all) to be updated to a modern era.

Can I watch Daredevil (2003) and Punisher (2004) without spoiling the Netflix series?

Yes. The movies you mention are distinct from the TV shows. Although they of course are based on the same source material, they are different interpretations.

I'll give you some more details on overlap/differences without spoiling anything.

Comparing Daredevil:

• Very similar origin story. This is unavoidable because the origin story directly explains Daredevil's powers, and also drives part of his character (in relation to his father).
• Although they have the same villain, they are very different incarnations of Kingpin. Comparing the two Kingpins is like comparing Jack Nicholson's Joker to Heath Ledger's Joker. They're about as different as they can be (while remaining within the source material).
• The movie mostly focuses on the hero persona (Daredevil). The person (Matt Murdock) isn't pulled into focus as much. Almost every side character knows Daredevil (not Matt Murdock). Matt Murdock's scenes generally only exist to further Daredevil's plotline.
• Comparatively, the TV Show focuses more on Matt Murdock than it does on Daredevil. The TV show is much less hero-infused than you'd expect from Marvel. Most side characters know Matt Murdock (not Daredevil). In most episode plots, Daredevil's scenes are used to assist Matt Murdock's plotline.
• The TV show questions the validity of Matt/Daredevil's approach. It questions vigilantism and the need for retribution. The movie, however, keeps Matt/Daredevil focused on a single goal, and only the side characters ask questions about vigilantism (which never really connects to the plot in a meaningful way).

I can draw an analogy to Batman. Val Kilmer and Michael Keaton's Batman movies mostly focus on Batman over Bruce Wayne, but the Christian Bale (Nolan) Batman movies focus more on Bruce Wayne and his ideologies.
I think this is mostly caused by the time period where the movies were released. Modern media puts a much heavier focus on gritty reality, compared to 10-20 years ago.

Comparing The Punisher:

• The origin story is different. Although the justification for becoming the Punisher is the same (loss of loved ones); the circumstances are completely different. In both cases, the circumstances heavily related to the main plot.
• Completely different main plot. The movie focuses on a local crime syndicate in a city. The TV show focuses on military/CIA/conspiracy theories.
• The movie's main focus is on defeating the bad guys; and the Punisher's questionable methods are hardly ever questioned (by the plot). Almost always, the Punisher responds to his environment, rather than provoking escalation. The Punisher is also very single-minded, and hardly ever shows signs of a different opinion, or questioning himself.
• The TV show, on the other hand, implicitly questions the validity of the Punisher's methods. While The Punisher himself is of course still focusing on the bad guys, he also drifts between different approaches. The show spends considerable screen time on side characters, whose plot points sometimes don't even relate to the main plot, but they usually indirectly question whether the Punisher is doing the right thing or not (thus making them on-topic for the viewer).
• The movie's characters were very one-dimensional (especially the innocent bystanders). The TV show has created a more gritty yet nuanced reality. Note: I loved the movie to death (and still do). I'm not saying the movie is bad, not at all, but the characters were a bit simple compared to now having seen the TV show.

Again, I can draw an analogy to Batman. The 90's Batman movies painted Batman as unquestionably good, and the villains as unquestionably evil. The same is true of the Punisher movie.
But the Nolan Batman movies focus more time on wondering if Bruce Wayne is doing the right thing, and not just using Batman as a way to vent his anger. Similarly, the Punisher TV show questions Frank Castle's state of mind and methods, instead of assuming they are unquestionably justified.

About the TV shows

Although the movies are unconnected to the TV shows, and the movies are unrelated to each other; the TV shows are connected.

The Punisher is first introduced in season 2 of the Daredevil TV show, and I highly suggest you watch this before you start with The Punisher. Without spoiling things, most of the existing Punisher lore is handled during Daredevil, and The Punisher picks up the story after the events that transpired in Daredevil.

It's not impossible to watch The Punisher (show) before Daredevil (show), but I highly advise against it. The Punisher is somewhat lighter on character exposition of Frank Castle exactly because his personality (and The Punisher's MO/justification) was exposed during Daredevil.